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← 4-2 · Use equilateral 60-degree angles and equal sides · Isosceles and Equilateral Angle Chaining

Use equilateral 60-degree angles and equal sides · 10 practice problems

4.G.A.24.MD.C.7

Generated variants — 10

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 answer: 19 cm

You want to make an equilateral triangle whose three side lengths add up to the same total as the isosceles triangle below. How many centimeters should each side of the equilateral triangle be?

24 cm 9 cm
Show solution

Understand

An isosceles triangle has two equal slant sides of 24 cm and a base of 9 cm. I need to build an equilateral triangle whose total side length (perimeter) is the same, and find how long each of its equal sides must be.

Givens
  • The isosceles triangle has two equal sides of 24 cm each
  • Its remaining (base) side is 9 cm
  • The equilateral triangle must have the same perimeter as the isosceles triangle
Unknowns
  • The length of one side of the equilateral triangle (in cm)
Constraints
  • An equilateral triangle has all three sides equal
  • Total perimeters of the two triangles must be equal

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

Split the task into two small steps: first find the isosceles triangle's perimeter by adding its three sides, then share that total equally among the equilateral triangle's three sides. Checking centimeters throughout keeps the setup correct.

Execute

#7 Identify Subproblems 4.MD.A.3
An isosceles triangle has two equal sides, so both slant sides are 24 cm. Add all three sides to get the perimeter.
24+24+9=57 cm24 + 24 + 9 = 57\ \text{cm}
Grade 4 students find a perimeter by adding the side lengths around the shape.
#7 Identify Subproblems 4.G.A.2
The equilateral triangle must have the same 57 cm perimeter, and all three of its sides are equal, so divide the perimeter by 3.
57÷3=19 cm57 \div 3 = 19\ \text{cm}
Equal sides means simply splitting the total length into 3 equal parts, a Grade 4 division idea.
#8 Analyze the Units 4.MD.A.1
Each side of the equilateral triangle is 19 cm. Units stay in centimeters from start to finish.
each side=19 cm\text{each side} = 19\ \text{cm}
Keeping the unit (cm) consistent confirms the answer is a length, not a count.
Answer: 19 cm

Review

Check: 19 + 19 + 19 = 57 cm, which matches the isosceles perimeter of 24 + 24 + 9 = 57 cm. Sharing the same total equally among three sides is exactly how an equilateral triangle keeps the same perimeter.

Guess and check (tool 6): try 19 cm per side, multiply by 3 to get 57 cm, and confirm it equals the isosceles perimeter; adjust the guess up or down if it didn't match.

Standards · min grade 4

  • 4.MD.A.3 Apply area and perimeter formulas for rectangles in real world and mathematical problems — Finding the perimeter of the isosceles triangle by adding its side lengths.
  • 4.G.A.2 Classify two-dimensional figures based on presence of parallel or perpendicular lines — Using the equilateral triangle's property that all three sides are equal.
  • 4.MD.A.1 Know relative sizes of measurement units and convert within a system — Keeping the length unit (centimeters) consistent throughout.
💡 This only needs Grade 4 perimeter-adding and equal-sharing you already know!
Variant 2 answer: 25 cm

You want to make an equilateral triangle whose three side lengths add up to the same total as the isosceles triangle below. How many centimeters should each side of the equilateral triangle be?

30 cm 15 cm
Show solution

Understand

An isosceles triangle has two equal slant sides of 30 cm and a base of 15 cm. I need to build an equilateral triangle whose total side length (perimeter) is the same, and find how long each of its equal sides must be.

Givens
  • The isosceles triangle has two equal sides of 30 cm each
  • Its remaining (base) side is 15 cm
  • The equilateral triangle must have the same perimeter as the isosceles triangle
Unknowns
  • The length of one side of the equilateral triangle (in cm)
Constraints
  • An equilateral triangle has all three sides equal
  • Total perimeters of the two triangles must be equal

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

Split the task into two small steps: first find the isosceles triangle's perimeter by adding its three sides, then share that total equally among the equilateral triangle's three sides. Checking centimeters throughout keeps the setup correct.

Execute

#7 Identify Subproblems 4.MD.A.3
An isosceles triangle has two equal sides, so both slant sides are 30 cm. Add all three sides to get the perimeter.
30+30+15=75 cm30 + 30 + 15 = 75\ \text{cm}
Grade 4 students find a perimeter by adding the side lengths around the shape.
#7 Identify Subproblems 4.G.A.2
The equilateral triangle must have the same 75 cm perimeter, and all three of its sides are equal, so divide the perimeter by 3.
75÷3=25 cm75 \div 3 = 25\ \text{cm}
Equal sides means simply splitting the total length into 3 equal parts, a Grade 4 division idea.
#8 Analyze the Units 4.MD.A.1
Each side of the equilateral triangle is 25 cm. Units stay in centimeters from start to finish.
each side=25 cm\text{each side} = 25\ \text{cm}
Keeping the unit (cm) consistent confirms the answer is a length, not a count.
Answer: 25 cm

Review

Check: 25 + 25 + 25 = 75 cm, which matches the isosceles perimeter of 30 + 30 + 15 = 75 cm. Sharing the same total equally among three sides is exactly how an equilateral triangle keeps the same perimeter.

Guess and check (tool 6): try 25 cm per side, multiply by 3 to get 75 cm, and confirm it equals the isosceles perimeter; adjust the guess up or down if it didn't match.

Standards · min grade 4

  • 4.MD.A.3 Apply area and perimeter formulas for rectangles in real world and mathematical problems — Finding the perimeter of the isosceles triangle by adding its side lengths.
  • 4.G.A.2 Classify two-dimensional figures based on presence of parallel or perpendicular lines — Using the equilateral triangle's property that all three sides are equal.
  • 4.MD.A.1 Know relative sizes of measurement units and convert within a system — Keeping the length unit (centimeters) consistent throughout.
💡 This only needs Grade 4 perimeter-adding and equal-sharing you already know!
Variant 3 answer: 15 cm

You want to make an equilateral triangle whose three side lengths add up to the same total as the isosceles triangle below. How many centimeters should each side of the equilateral triangle be?

16 cm 13 cm
Show solution

Understand

An isosceles triangle has two equal slant sides of 16 cm and a base of 13 cm. I need to build an equilateral triangle whose total side length (perimeter) is the same, and find how long each of its equal sides must be.

Givens
  • The isosceles triangle has two equal sides of 16 cm each
  • Its remaining (base) side is 13 cm
  • The equilateral triangle must have the same perimeter as the isosceles triangle
Unknowns
  • The length of one side of the equilateral triangle (in cm)
Constraints
  • An equilateral triangle has all three sides equal
  • Total perimeters of the two triangles must be equal

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

Split the task into two small steps: first find the isosceles triangle's perimeter by adding its three sides, then share that total equally among the equilateral triangle's three sides. Checking centimeters throughout keeps the setup correct.

Execute

#7 Identify Subproblems 4.MD.A.3
An isosceles triangle has two equal sides, so both slant sides are 16 cm. Add all three sides to get the perimeter.
16+16+13=45 cm16 + 16 + 13 = 45\ \text{cm}
Grade 4 students find a perimeter by adding the side lengths around the shape.
#7 Identify Subproblems 4.G.A.2
The equilateral triangle must have the same 45 cm perimeter, and all three of its sides are equal, so divide the perimeter by 3.
45÷3=15 cm45 \div 3 = 15\ \text{cm}
Equal sides means simply splitting the total length into 3 equal parts, a Grade 4 division idea.
#8 Analyze the Units 4.MD.A.1
Each side of the equilateral triangle is 15 cm. Units stay in centimeters from start to finish.
each side=15 cm\text{each side} = 15\ \text{cm}
Keeping the unit (cm) consistent confirms the answer is a length, not a count.
Answer: 15 cm

Review

Check: 15 + 15 + 15 = 45 cm, which matches the isosceles perimeter of 16 + 16 + 13 = 45 cm. Sharing the same total equally among three sides is exactly how an equilateral triangle keeps the same perimeter.

Guess and check (tool 6): try 15 cm per side, multiply by 3 to get 45 cm, and confirm it equals the isosceles perimeter; adjust the guess up or down if it didn't match.

Standards · min grade 4

  • 4.MD.A.3 Apply area and perimeter formulas for rectangles in real world and mathematical problems — Finding the perimeter of the isosceles triangle by adding its side lengths.
  • 4.G.A.2 Classify two-dimensional figures based on presence of parallel or perpendicular lines — Using the equilateral triangle's property that all three sides are equal.
  • 4.MD.A.1 Know relative sizes of measurement units and convert within a system — Keeping the length unit (centimeters) consistent throughout.
💡 This only needs Grade 4 perimeter-adding and equal-sharing you already know!
Variant 4 answer: 8 cm

You want to make an equilateral triangle whose three side lengths add up to the same total as the isosceles triangle below. How many centimeters should each side of the equilateral triangle be?

9 cm 6 cm
Show solution

Understand

An isosceles triangle has two equal slant sides of 9 cm and a base of 6 cm. I need to build an equilateral triangle whose total side length (perimeter) is the same, and find how long each of its equal sides must be.

Givens
  • The isosceles triangle has two equal sides of 9 cm each
  • Its remaining (base) side is 6 cm
  • The equilateral triangle must have the same perimeter as the isosceles triangle
Unknowns
  • The length of one side of the equilateral triangle (in cm)
Constraints
  • An equilateral triangle has all three sides equal
  • Total perimeters of the two triangles must be equal

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

Split the task into two small steps: first find the isosceles triangle's perimeter by adding its three sides, then share that total equally among the equilateral triangle's three sides. Checking centimeters throughout keeps the setup correct.

Execute

#7 Identify Subproblems 4.MD.A.3
An isosceles triangle has two equal sides, so both slant sides are 9 cm. Add all three sides to get the perimeter.
9+9+6=24 cm9 + 9 + 6 = 24\ \text{cm}
Grade 4 students find a perimeter by adding the side lengths around the shape.
#7 Identify Subproblems 4.G.A.2
The equilateral triangle must have the same 24 cm perimeter, and all three of its sides are equal, so divide the perimeter by 3.
24÷3=8 cm24 \div 3 = 8\ \text{cm}
Equal sides means simply splitting the total length into 3 equal parts, a Grade 4 division idea.
#8 Analyze the Units 4.MD.A.1
Each side of the equilateral triangle is 8 cm. Units stay in centimeters from start to finish.
each side=8 cm\text{each side} = 8\ \text{cm}
Keeping the unit (cm) consistent confirms the answer is a length, not a count.
Answer: 8 cm

Review

Check: 8 + 8 + 8 = 24 cm, which matches the isosceles perimeter of 9 + 9 + 6 = 24 cm. Sharing the same total equally among three sides is exactly how an equilateral triangle keeps the same perimeter.

Guess and check (tool 6): try 8 cm per side, multiply by 3 to get 24 cm, and confirm it equals the isosceles perimeter; adjust the guess up or down if it didn't match.

Standards · min grade 4

  • 4.MD.A.3 Apply area and perimeter formulas for rectangles in real world and mathematical problems — Finding the perimeter of the isosceles triangle by adding its side lengths.
  • 4.G.A.2 Classify two-dimensional figures based on presence of parallel or perpendicular lines — Using the equilateral triangle's property that all three sides are equal.
  • 4.MD.A.1 Know relative sizes of measurement units and convert within a system — Keeping the length unit (centimeters) consistent throughout.
💡 This only needs Grade 4 perimeter-adding and equal-sharing you already know!
Variant 5 answer: 22 cm

You want to make an equilateral triangle whose three side lengths add up to the same total as the isosceles triangle below. How many centimeters should each side of the equilateral triangle be?

27 cm 12 cm
Show solution

Understand

An isosceles triangle has two equal slant sides of 27 cm and a base of 12 cm. I need to build an equilateral triangle whose total side length (perimeter) is the same, and find how long each of its equal sides must be.

Givens
  • The isosceles triangle has two equal sides of 27 cm each
  • Its remaining (base) side is 12 cm
  • The equilateral triangle must have the same perimeter as the isosceles triangle
Unknowns
  • The length of one side of the equilateral triangle (in cm)
Constraints
  • An equilateral triangle has all three sides equal
  • Total perimeters of the two triangles must be equal

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

Split the task into two small steps: first find the isosceles triangle's perimeter by adding its three sides, then share that total equally among the equilateral triangle's three sides. Checking centimeters throughout keeps the setup correct.

Execute

#7 Identify Subproblems 4.MD.A.3
An isosceles triangle has two equal sides, so both slant sides are 27 cm. Add all three sides to get the perimeter.
27+27+12=66 cm27 + 27 + 12 = 66\ \text{cm}
Grade 4 students find a perimeter by adding the side lengths around the shape.
#7 Identify Subproblems 4.G.A.2
The equilateral triangle must have the same 66 cm perimeter, and all three of its sides are equal, so divide the perimeter by 3.
66÷3=22 cm66 \div 3 = 22\ \text{cm}
Equal sides means simply splitting the total length into 3 equal parts, a Grade 4 division idea.
#8 Analyze the Units 4.MD.A.1
Each side of the equilateral triangle is 22 cm. Units stay in centimeters from start to finish.
each side=22 cm\text{each side} = 22\ \text{cm}
Keeping the unit (cm) consistent confirms the answer is a length, not a count.
Answer: 22 cm

Review

Check: 22 + 22 + 22 = 66 cm, which matches the isosceles perimeter of 27 + 27 + 12 = 66 cm. Sharing the same total equally among three sides is exactly how an equilateral triangle keeps the same perimeter.

Guess and check (tool 6): try 22 cm per side, multiply by 3 to get 66 cm, and confirm it equals the isosceles perimeter; adjust the guess up or down if it didn't match.

Standards · min grade 4

  • 4.MD.A.3 Apply area and perimeter formulas for rectangles in real world and mathematical problems — Finding the perimeter of the isosceles triangle by adding its side lengths.
  • 4.G.A.2 Classify two-dimensional figures based on presence of parallel or perpendicular lines — Using the equilateral triangle's property that all three sides are equal.
  • 4.MD.A.1 Know relative sizes of measurement units and convert within a system — Keeping the length unit (centimeters) consistent throughout.
💡 This only needs Grade 4 perimeter-adding and equal-sharing you already know!
Variant 6 answer: 13 cm

You want to make an equilateral triangle whose three side lengths add up to the same total as the isosceles triangle below. How many centimeters should each side of the equilateral triangle be?

15 cm 9 cm
Show solution

Understand

An isosceles triangle has two equal slant sides of 15 cm and a base of 9 cm. I need to build an equilateral triangle whose total side length (perimeter) is the same, and find how long each of its equal sides must be.

Givens
  • The isosceles triangle has two equal sides of 15 cm each
  • Its remaining (base) side is 9 cm
  • The equilateral triangle must have the same perimeter as the isosceles triangle
Unknowns
  • The length of one side of the equilateral triangle (in cm)
Constraints
  • An equilateral triangle has all three sides equal
  • Total perimeters of the two triangles must be equal

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

Split the task into two small steps: first find the isosceles triangle's perimeter by adding its three sides, then share that total equally among the equilateral triangle's three sides. Checking centimeters throughout keeps the setup correct.

Execute

#7 Identify Subproblems 4.MD.A.3
An isosceles triangle has two equal sides, so both slant sides are 15 cm. Add all three sides to get the perimeter.
15+15+9=39 cm15 + 15 + 9 = 39\ \text{cm}
Grade 4 students find a perimeter by adding the side lengths around the shape.
#7 Identify Subproblems 4.G.A.2
The equilateral triangle must have the same 39 cm perimeter, and all three of its sides are equal, so divide the perimeter by 3.
39÷3=13 cm39 \div 3 = 13\ \text{cm}
Equal sides means simply splitting the total length into 3 equal parts, a Grade 4 division idea.
#8 Analyze the Units 4.MD.A.1
Each side of the equilateral triangle is 13 cm. Units stay in centimeters from start to finish.
each side=13 cm\text{each side} = 13\ \text{cm}
Keeping the unit (cm) consistent confirms the answer is a length, not a count.
Answer: 13 cm

Review

Check: 13 + 13 + 13 = 39 cm, which matches the isosceles perimeter of 15 + 15 + 9 = 39 cm. Sharing the same total equally among three sides is exactly how an equilateral triangle keeps the same perimeter.

Guess and check (tool 6): try 13 cm per side, multiply by 3 to get 39 cm, and confirm it equals the isosceles perimeter; adjust the guess up or down if it didn't match.

Standards · min grade 4

  • 4.MD.A.3 Apply area and perimeter formulas for rectangles in real world and mathematical problems — Finding the perimeter of the isosceles triangle by adding its side lengths.
  • 4.G.A.2 Classify two-dimensional figures based on presence of parallel or perpendicular lines — Using the equilateral triangle's property that all three sides are equal.
  • 4.MD.A.1 Know relative sizes of measurement units and convert within a system — Keeping the length unit (centimeters) consistent throughout.
💡 This only needs Grade 4 perimeter-adding and equal-sharing you already know!
Variant 7 answer: 17 cm

You want to make an equilateral triangle whose three side lengths add up to the same total as the isosceles triangle below. How many centimeters should each side of the equilateral triangle be?

20 cm 11 cm
Show solution

Understand

An isosceles triangle has two equal slant sides of 20 cm and a base of 11 cm. I need to build an equilateral triangle whose total side length (perimeter) is the same, and find how long each of its equal sides must be.

Givens
  • The isosceles triangle has two equal sides of 20 cm each
  • Its remaining (base) side is 11 cm
  • The equilateral triangle must have the same perimeter as the isosceles triangle
Unknowns
  • The length of one side of the equilateral triangle (in cm)
Constraints
  • An equilateral triangle has all three sides equal
  • Total perimeters of the two triangles must be equal

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

Split the task into two small steps: first find the isosceles triangle's perimeter by adding its three sides, then share that total equally among the equilateral triangle's three sides. Checking centimeters throughout keeps the setup correct.

Execute

#7 Identify Subproblems 4.MD.A.3
An isosceles triangle has two equal sides, so both slant sides are 20 cm. Add all three sides to get the perimeter.
20+20+11=51 cm20 + 20 + 11 = 51\ \text{cm}
Grade 4 students find a perimeter by adding the side lengths around the shape.
#7 Identify Subproblems 4.G.A.2
The equilateral triangle must have the same 51 cm perimeter, and all three of its sides are equal, so divide the perimeter by 3.
51÷3=17 cm51 \div 3 = 17\ \text{cm}
Equal sides means simply splitting the total length into 3 equal parts, a Grade 4 division idea.
#8 Analyze the Units 4.MD.A.1
Each side of the equilateral triangle is 17 cm. Units stay in centimeters from start to finish.
each side=17 cm\text{each side} = 17\ \text{cm}
Keeping the unit (cm) consistent confirms the answer is a length, not a count.
Answer: 17 cm

Review

Check: 17 + 17 + 17 = 51 cm, which matches the isosceles perimeter of 20 + 20 + 11 = 51 cm. Sharing the same total equally among three sides is exactly how an equilateral triangle keeps the same perimeter.

Guess and check (tool 6): try 17 cm per side, multiply by 3 to get 51 cm, and confirm it equals the isosceles perimeter; adjust the guess up or down if it didn't match.

Standards · min grade 4

  • 4.MD.A.3 Apply area and perimeter formulas for rectangles in real world and mathematical problems — Finding the perimeter of the isosceles triangle by adding its side lengths.
  • 4.G.A.2 Classify two-dimensional figures based on presence of parallel or perpendicular lines — Using the equilateral triangle's property that all three sides are equal.
  • 4.MD.A.1 Know relative sizes of measurement units and convert within a system — Keeping the length unit (centimeters) consistent throughout.
💡 This only needs Grade 4 perimeter-adding and equal-sharing you already know!
Variant 8 answer: 14 cm

You want to make an equilateral triangle whose three side lengths add up to the same total as the isosceles triangle below. How many centimeters should each side of the equilateral triangle be?

18 cm 6 cm
Show solution

Understand

An isosceles triangle has two equal slant sides of 18 cm and a base of 6 cm. I need to build an equilateral triangle whose total side length (perimeter) is the same, and find how long each of its equal sides must be.

Givens
  • The isosceles triangle has two equal sides of 18 cm each
  • Its remaining (base) side is 6 cm
  • The equilateral triangle must have the same perimeter as the isosceles triangle
Unknowns
  • The length of one side of the equilateral triangle (in cm)
Constraints
  • An equilateral triangle has all three sides equal
  • Total perimeters of the two triangles must be equal

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

Split the task into two small steps: first find the isosceles triangle's perimeter by adding its three sides, then share that total equally among the equilateral triangle's three sides. Checking centimeters throughout keeps the setup correct.

Execute

#7 Identify Subproblems 4.MD.A.3
An isosceles triangle has two equal sides, so both slant sides are 18 cm. Add all three sides to get the perimeter.
18+18+6=42 cm18 + 18 + 6 = 42\ \text{cm}
Grade 4 students find a perimeter by adding the side lengths around the shape.
#7 Identify Subproblems 4.G.A.2
The equilateral triangle must have the same 42 cm perimeter, and all three of its sides are equal, so divide the perimeter by 3.
42÷3=14 cm42 \div 3 = 14\ \text{cm}
Equal sides means simply splitting the total length into 3 equal parts, a Grade 4 division idea.
#8 Analyze the Units 4.MD.A.1
Each side of the equilateral triangle is 14 cm. Units stay in centimeters from start to finish.
each side=14 cm\text{each side} = 14\ \text{cm}
Keeping the unit (cm) consistent confirms the answer is a length, not a count.
Answer: 14 cm

Review

Check: 14 + 14 + 14 = 42 cm, which matches the isosceles perimeter of 18 + 18 + 6 = 42 cm. Sharing the same total equally among three sides is exactly how an equilateral triangle keeps the same perimeter.

Guess and check (tool 6): try 14 cm per side, multiply by 3 to get 42 cm, and confirm it equals the isosceles perimeter; adjust the guess up or down if it didn't match.

Standards · min grade 4

  • 4.MD.A.3 Apply area and perimeter formulas for rectangles in real world and mathematical problems — Finding the perimeter of the isosceles triangle by adding its side lengths.
  • 4.G.A.2 Classify two-dimensional figures based on presence of parallel or perpendicular lines — Using the equilateral triangle's property that all three sides are equal.
  • 4.MD.A.1 Know relative sizes of measurement units and convert within a system — Keeping the length unit (centimeters) consistent throughout.
💡 This only needs Grade 4 perimeter-adding and equal-sharing you already know!
Variant 9 answer: 11 cm

You want to make an equilateral triangle whose three side lengths add up to the same total as the isosceles triangle below. How many centimeters should each side of the equilateral triangle be?

12 cm 9 cm
Show solution

Understand

An isosceles triangle has two equal slant sides of 12 cm and a base of 9 cm. I need to build an equilateral triangle whose total side length (perimeter) is the same, and find how long each of its equal sides must be.

Givens
  • The isosceles triangle has two equal sides of 12 cm each
  • Its remaining (base) side is 9 cm
  • The equilateral triangle must have the same perimeter as the isosceles triangle
Unknowns
  • The length of one side of the equilateral triangle (in cm)
Constraints
  • An equilateral triangle has all three sides equal
  • Total perimeters of the two triangles must be equal

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

Split the task into two small steps: first find the isosceles triangle's perimeter by adding its three sides, then share that total equally among the equilateral triangle's three sides. Checking centimeters throughout keeps the setup correct.

Execute

#7 Identify Subproblems 4.MD.A.3
An isosceles triangle has two equal sides, so both slant sides are 12 cm. Add all three sides to get the perimeter.
12+12+9=33 cm12 + 12 + 9 = 33\ \text{cm}
Grade 4 students find a perimeter by adding the side lengths around the shape.
#7 Identify Subproblems 4.G.A.2
The equilateral triangle must have the same 33 cm perimeter, and all three of its sides are equal, so divide the perimeter by 3.
33÷3=11 cm33 \div 3 = 11\ \text{cm}
Equal sides means simply splitting the total length into 3 equal parts, a Grade 4 division idea.
#8 Analyze the Units 4.MD.A.1
Each side of the equilateral triangle is 11 cm. Units stay in centimeters from start to finish.
each side=11 cm\text{each side} = 11\ \text{cm}
Keeping the unit (cm) consistent confirms the answer is a length, not a count.
Answer: 11 cm

Review

Check: 11 + 11 + 11 = 33 cm, which matches the isosceles perimeter of 12 + 12 + 9 = 33 cm. Sharing the same total equally among three sides is exactly how an equilateral triangle keeps the same perimeter.

Guess and check (tool 6): try 11 cm per side, multiply by 3 to get 33 cm, and confirm it equals the isosceles perimeter; adjust the guess up or down if it didn't match.

Standards · min grade 4

  • 4.MD.A.3 Apply area and perimeter formulas for rectangles in real world and mathematical problems — Finding the perimeter of the isosceles triangle by adding its side lengths.
  • 4.G.A.2 Classify two-dimensional figures based on presence of parallel or perpendicular lines — Using the equilateral triangle's property that all three sides are equal.
  • 4.MD.A.1 Know relative sizes of measurement units and convert within a system — Keeping the length unit (centimeters) consistent throughout.
💡 This only needs Grade 4 perimeter-adding and equal-sharing you already know!
Variant 10 answer: 19 cm

You want to make an equilateral triangle whose three side lengths add up to the same total as the isosceles triangle below. How many centimeters should each side of the equilateral triangle be?

21 cm 15 cm
Show solution

Understand

An isosceles triangle has two equal slant sides of 21 cm and a base of 15 cm. I need to build an equilateral triangle whose total side length (perimeter) is the same, and find how long each of its equal sides must be.

Givens
  • The isosceles triangle has two equal sides of 21 cm each
  • Its remaining (base) side is 15 cm
  • The equilateral triangle must have the same perimeter as the isosceles triangle
Unknowns
  • The length of one side of the equilateral triangle (in cm)
Constraints
  • An equilateral triangle has all three sides equal
  • Total perimeters of the two triangles must be equal

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

Split the task into two small steps: first find the isosceles triangle's perimeter by adding its three sides, then share that total equally among the equilateral triangle's three sides. Checking centimeters throughout keeps the setup correct.

Execute

#7 Identify Subproblems 4.MD.A.3
An isosceles triangle has two equal sides, so both slant sides are 21 cm. Add all three sides to get the perimeter.
21+21+15=57 cm21 + 21 + 15 = 57\ \text{cm}
Grade 4 students find a perimeter by adding the side lengths around the shape.
#7 Identify Subproblems 4.G.A.2
The equilateral triangle must have the same 57 cm perimeter, and all three of its sides are equal, so divide the perimeter by 3.
57÷3=19 cm57 \div 3 = 19\ \text{cm}
Equal sides means simply splitting the total length into 3 equal parts, a Grade 4 division idea.
#8 Analyze the Units 4.MD.A.1
Each side of the equilateral triangle is 19 cm. Units stay in centimeters from start to finish.
each side=19 cm\text{each side} = 19\ \text{cm}
Keeping the unit (cm) consistent confirms the answer is a length, not a count.
Answer: 19 cm

Review

Check: 19 + 19 + 19 = 57 cm, which matches the isosceles perimeter of 21 + 21 + 15 = 57 cm. Sharing the same total equally among three sides is exactly how an equilateral triangle keeps the same perimeter.

Guess and check (tool 6): try 19 cm per side, multiply by 3 to get 57 cm, and confirm it equals the isosceles perimeter; adjust the guess up or down if it didn't match.

Standards · min grade 4

  • 4.MD.A.3 Apply area and perimeter formulas for rectangles in real world and mathematical problems — Finding the perimeter of the isosceles triangle by adding its side lengths.
  • 4.G.A.2 Classify two-dimensional figures based on presence of parallel or perpendicular lines — Using the equilateral triangle's property that all three sides are equal.
  • 4.MD.A.1 Know relative sizes of measurement units and convert within a system — Keeping the length unit (centimeters) consistent throughout.
💡 This only needs Grade 4 perimeter-adding and equal-sharing you already know!