Practice · Perimeter as decimal side sums minus overlaps · Sensim Math

Variant 1 answer: 2 m

Using a $3.5\ \text{m}$ length of wire without overlapping, you bent it to make one equilateral triangle like the one shown. How many meters of wire are left over?

(Figure: one equilateral triangle, with one side labeled $0.5\ \text{m}$ .)

Show solution

Understand

A 3.5 m piece of wire is bent (no overlap) into one equilateral triangle whose side is 0.5 m. I need to find how much wire is left over after making the triangle.

Givens

Total wire length is 3.5 m.
The shape made is an equilateral triangle (all three sides equal).
Each side of the triangle is 0.5 m.
No wire overlaps when bending.

Unknowns

The length of wire left over, in meters.

Constraints

An equilateral triangle has exactly 3 equal sides.
Wire used equals the triangle's perimeter; leftover = total - perimeter.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram#8 Analyze the Units

Break the task into two small steps: first the perimeter (a side-length sum for an equilateral triangle), then a subtraction from the total wire. The figure shows one labeled side, and all sides are equal, so the perimeter is 3 copies of the side. Keeping the meters consistent guards against place-value slips with decimals.

Execute

#7 Identify Subproblems 5.NBT.B.7

An equilateral triangle has three equal sides of 0.5 m, so the wire used is the sum of the three sides.

0.5 + 0.5 + 0.5 = 0.5 \times 3 = 1.5 \text{ m}

Adding three equal decimals is the same as multiplying by 3; lining up the hundredths keeps the place values straight.

#7 Identify Subproblems 5.NBT.B.7

The leftover wire is the total length minus the wire used for the triangle.

3.5 - 1.5 = 2 \text{ m}

Subtract the used wire from the total, regrouping the decimals just like money amounts.

Answer: 2 m

Review

The triangle uses 1.5 m out of the 3.5 m wire. Check: 1.5 + 2 = 3.5 m, exactly the original wire, so 2 m left over is consistent.

Use Draw a Diagram (tool 1): sketch the wire as a number line, mark off three side-length hops for the triangle, and read the remaining length.

Standards · min grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the side by 3 for the perimeter and subtracting that from the total.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Treating the wire used as the triangle's perimeter (sum of side lengths).

💡 Add up the three equal sides, then subtract from the total: leftover wire is just a tidy decimal subtraction you already know!

Variant 2 answer: 2.26 m

Using a $4\ \text{m}$ length of wire without overlapping, you bent it to make one equilateral triangle like the one shown. How many meters of wire are left over?

(Figure: one equilateral triangle, with one side labeled $0.58\ \text{m}$ .)

Show solution

Understand

A 4 m piece of wire is bent (no overlap) into one equilateral triangle whose side is 0.58 m. I need to find how much wire is left over after making the triangle.

Givens

Total wire length is 4 m.
The shape made is an equilateral triangle (all three sides equal).
Each side of the triangle is 0.58 m.
No wire overlaps when bending.

Unknowns

The length of wire left over, in meters.

Constraints

An equilateral triangle has exactly 3 equal sides.
Wire used equals the triangle's perimeter; leftover = total - perimeter.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram#8 Analyze the Units

Break the task into two small steps: first the perimeter (a side-length sum for an equilateral triangle), then a subtraction from the total wire. The figure shows one labeled side, and all sides are equal, so the perimeter is 3 copies of the side. Keeping the meters consistent guards against place-value slips with decimals.

Execute

#7 Identify Subproblems 5.NBT.B.7

An equilateral triangle has three equal sides of 0.58 m, so the wire used is the sum of the three sides.

0.58 + 0.58 + 0.58 = 0.58 \times 3 = 1.74 \text{ m}

Adding three equal decimals is the same as multiplying by 3; lining up the hundredths keeps the place values straight.

#7 Identify Subproblems 5.NBT.B.7

The leftover wire is the total length minus the wire used for the triangle.

4 - 1.74 = 2.26 \text{ m}

Subtract the used wire from the total, regrouping the decimals just like money amounts.

Answer: 2.26 m

Review

The triangle uses 1.74 m out of the 4 m wire. Check: 1.74 + 2.26 = 4 m, exactly the original wire, so 2.26 m left over is consistent.

Use Draw a Diagram (tool 1): sketch the wire as a number line, mark off three side-length hops for the triangle, and read the remaining length.

Standards · min grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the side by 3 for the perimeter and subtracting that from the total.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Treating the wire used as the triangle's perimeter (sum of side lengths).

💡 Add up the three equal sides, then subtract from the total: leftover wire is just a tidy decimal subtraction you already know!

Variant 3 answer: 5.5 m

Using a $10\ \text{m}$ length of wire without overlapping, you bent it to make one equilateral triangle like the one shown. How many meters of wire are left over?

(Figure: one equilateral triangle, with one side labeled $1.5\ \text{m}$ .)

Show solution

Understand

A 10 m piece of wire is bent (no overlap) into one equilateral triangle whose side is 1.5 m. I need to find how much wire is left over after making the triangle.

Givens

Total wire length is 10 m.
The shape made is an equilateral triangle (all three sides equal).
Each side of the triangle is 1.5 m.
No wire overlaps when bending.

Unknowns

The length of wire left over, in meters.

Constraints

An equilateral triangle has exactly 3 equal sides.
Wire used equals the triangle's perimeter; leftover = total - perimeter.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram#8 Analyze the Units

Break the task into two small steps: first the perimeter (a side-length sum for an equilateral triangle), then a subtraction from the total wire. The figure shows one labeled side, and all sides are equal, so the perimeter is 3 copies of the side. Keeping the meters consistent guards against place-value slips with decimals.

Execute

#7 Identify Subproblems 5.NBT.B.7

An equilateral triangle has three equal sides of 1.5 m, so the wire used is the sum of the three sides.

1.5 + 1.5 + 1.5 = 1.5 \times 3 = 4.5 \text{ m}

Adding three equal decimals is the same as multiplying by 3; lining up the hundredths keeps the place values straight.

#7 Identify Subproblems 5.NBT.B.7

The leftover wire is the total length minus the wire used for the triangle.

10 - 4.5 = 5.5 \text{ m}

Subtract the used wire from the total, regrouping the decimals just like money amounts.

Answer: 5.5 m

Review

The triangle uses 4.5 m out of the 10 m wire. Check: 4.5 + 5.5 = 10 m, exactly the original wire, so 5.5 m left over is consistent.

Use Draw a Diagram (tool 1): sketch the wire as a number line, mark off three side-length hops for the triangle, and read the remaining length.

Standards · min grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the side by 3 for the perimeter and subtracting that from the total.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Treating the wire used as the triangle's perimeter (sum of side lengths).

💡 Add up the three equal sides, then subtract from the total: leftover wire is just a tidy decimal subtraction you already know!

Variant 4 answer: 1.65 m

Using a $3\ \text{m}$ length of wire without overlapping, you bent it to make one equilateral triangle like the one shown. How many meters of wire are left over?

(Figure: one equilateral triangle, with one side labeled $0.45\ \text{m}$ .)

Show solution

Understand

A 3 m piece of wire is bent (no overlap) into one equilateral triangle whose side is 0.45 m. I need to find how much wire is left over after making the triangle.

Givens

Total wire length is 3 m.
The shape made is an equilateral triangle (all three sides equal).
Each side of the triangle is 0.45 m.
No wire overlaps when bending.

Unknowns

The length of wire left over, in meters.

Constraints

An equilateral triangle has exactly 3 equal sides.
Wire used equals the triangle's perimeter; leftover = total - perimeter.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram#8 Analyze the Units

Break the task into two small steps: first the perimeter (a side-length sum for an equilateral triangle), then a subtraction from the total wire. The figure shows one labeled side, and all sides are equal, so the perimeter is 3 copies of the side. Keeping the meters consistent guards against place-value slips with decimals.

Execute

#7 Identify Subproblems 5.NBT.B.7

An equilateral triangle has three equal sides of 0.45 m, so the wire used is the sum of the three sides.

0.45 + 0.45 + 0.45 = 0.45 \times 3 = 1.35 \text{ m}

Adding three equal decimals is the same as multiplying by 3; lining up the hundredths keeps the place values straight.

#7 Identify Subproblems 5.NBT.B.7

The leftover wire is the total length minus the wire used for the triangle.

3 - 1.35 = 1.65 \text{ m}

Subtract the used wire from the total, regrouping the decimals just like money amounts.

Answer: 1.65 m

Review

The triangle uses 1.35 m out of the 3 m wire. Check: 1.35 + 1.65 = 3 m, exactly the original wire, so 1.65 m left over is consistent.

Use Draw a Diagram (tool 1): sketch the wire as a number line, mark off three side-length hops for the triangle, and read the remaining length.

Standards · min grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the side by 3 for the perimeter and subtracting that from the total.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Treating the wire used as the triangle's perimeter (sum of side lengths).

💡 Add up the three equal sides, then subtract from the total: leftover wire is just a tidy decimal subtraction you already know!

Variant 5 answer: 4.25 m

Using a $8\ \text{m}$ length of wire without overlapping, you bent it to make one equilateral triangle like the one shown. How many meters of wire are left over?

(Figure: one equilateral triangle, with one side labeled $1.25\ \text{m}$ .)

Show solution

Understand

A 8 m piece of wire is bent (no overlap) into one equilateral triangle whose side is 1.25 m. I need to find how much wire is left over after making the triangle.

Givens

Total wire length is 8 m.
The shape made is an equilateral triangle (all three sides equal).
Each side of the triangle is 1.25 m.
No wire overlaps when bending.

Unknowns

The length of wire left over, in meters.

Constraints

An equilateral triangle has exactly 3 equal sides.
Wire used equals the triangle's perimeter; leftover = total - perimeter.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram#8 Analyze the Units

Break the task into two small steps: first the perimeter (a side-length sum for an equilateral triangle), then a subtraction from the total wire. The figure shows one labeled side, and all sides are equal, so the perimeter is 3 copies of the side. Keeping the meters consistent guards against place-value slips with decimals.

Execute

#7 Identify Subproblems 5.NBT.B.7

An equilateral triangle has three equal sides of 1.25 m, so the wire used is the sum of the three sides.

1.25 + 1.25 + 1.25 = 1.25 \times 3 = 3.75 \text{ m}

Adding three equal decimals is the same as multiplying by 3; lining up the hundredths keeps the place values straight.

#7 Identify Subproblems 5.NBT.B.7

The leftover wire is the total length minus the wire used for the triangle.

8 - 3.75 = 4.25 \text{ m}

Subtract the used wire from the total, regrouping the decimals just like money amounts.

Answer: 4.25 m

Review

The triangle uses 3.75 m out of the 8 m wire. Check: 3.75 + 4.25 = 8 m, exactly the original wire, so 4.25 m left over is consistent.

Use Draw a Diagram (tool 1): sketch the wire as a number line, mark off three side-length hops for the triangle, and read the remaining length.

Standards · min grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the side by 3 for the perimeter and subtracting that from the total.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Treating the wire used as the triangle's perimeter (sum of side lengths).

💡 Add up the three equal sides, then subtract from the total: leftover wire is just a tidy decimal subtraction you already know!

Variant 6 answer: 2.7 m

Using a $4.5\ \text{m}$ length of wire without overlapping, you bent it to make one equilateral triangle like the one shown. How many meters of wire are left over?

(Figure: one equilateral triangle, with one side labeled $0.6\ \text{m}$ .)

Show solution

Understand

A 4.5 m piece of wire is bent (no overlap) into one equilateral triangle whose side is 0.6 m. I need to find how much wire is left over after making the triangle.

Givens

Total wire length is 4.5 m.
The shape made is an equilateral triangle (all three sides equal).
Each side of the triangle is 0.6 m.
No wire overlaps when bending.

Unknowns

The length of wire left over, in meters.

Constraints

An equilateral triangle has exactly 3 equal sides.
Wire used equals the triangle's perimeter; leftover = total - perimeter.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram#8 Analyze the Units

Break the task into two small steps: first the perimeter (a side-length sum for an equilateral triangle), then a subtraction from the total wire. The figure shows one labeled side, and all sides are equal, so the perimeter is 3 copies of the side. Keeping the meters consistent guards against place-value slips with decimals.

Execute

#7 Identify Subproblems 5.NBT.B.7

An equilateral triangle has three equal sides of 0.6 m, so the wire used is the sum of the three sides.

0.6 + 0.6 + 0.6 = 0.6 \times 3 = 1.8 \text{ m}

Adding three equal decimals is the same as multiplying by 3; lining up the hundredths keeps the place values straight.

#7 Identify Subproblems 5.NBT.B.7

The leftover wire is the total length minus the wire used for the triangle.

4.5 - 1.8 = 2.7 \text{ m}

Subtract the used wire from the total, regrouping the decimals just like money amounts.

Answer: 2.7 m

Review

The triangle uses 1.8 m out of the 4.5 m wire. Check: 1.8 + 2.7 = 4.5 m, exactly the original wire, so 2.7 m left over is consistent.

Use Draw a Diagram (tool 1): sketch the wire as a number line, mark off three side-length hops for the triangle, and read the remaining length.

Standards · min grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the side by 3 for the perimeter and subtracting that from the total.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Treating the wire used as the triangle's perimeter (sum of side lengths).

💡 Add up the three equal sides, then subtract from the total: leftover wire is just a tidy decimal subtraction you already know!

Variant 7 answer: 1.6 m

Using a $4\ \text{m}$ length of wire without overlapping, you bent it to make one equilateral triangle like the one shown. How many meters of wire are left over?

(Figure: one equilateral triangle, with one side labeled $0.8\ \text{m}$ .)

Show solution

Understand

A 4 m piece of wire is bent (no overlap) into one equilateral triangle whose side is 0.8 m. I need to find how much wire is left over after making the triangle.

Givens

Total wire length is 4 m.
The shape made is an equilateral triangle (all three sides equal).
Each side of the triangle is 0.8 m.
No wire overlaps when bending.

Unknowns

The length of wire left over, in meters.

Constraints

An equilateral triangle has exactly 3 equal sides.
Wire used equals the triangle's perimeter; leftover = total - perimeter.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram#8 Analyze the Units

Break the task into two small steps: first the perimeter (a side-length sum for an equilateral triangle), then a subtraction from the total wire. The figure shows one labeled side, and all sides are equal, so the perimeter is 3 copies of the side. Keeping the meters consistent guards against place-value slips with decimals.

Execute

#7 Identify Subproblems 5.NBT.B.7

An equilateral triangle has three equal sides of 0.8 m, so the wire used is the sum of the three sides.

0.8 + 0.8 + 0.8 = 0.8 \times 3 = 2.4 \text{ m}

Adding three equal decimals is the same as multiplying by 3; lining up the hundredths keeps the place values straight.

#7 Identify Subproblems 5.NBT.B.7

The leftover wire is the total length minus the wire used for the triangle.

4 - 2.4 = 1.6 \text{ m}

Subtract the used wire from the total, regrouping the decimals just like money amounts.

Answer: 1.6 m

Review

The triangle uses 2.4 m out of the 4 m wire. Check: 2.4 + 1.6 = 4 m, exactly the original wire, so 1.6 m left over is consistent.

Use Draw a Diagram (tool 1): sketch the wire as a number line, mark off three side-length hops for the triangle, and read the remaining length.

Standards · min grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the side by 3 for the perimeter and subtracting that from the total.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Treating the wire used as the triangle's perimeter (sum of side lengths).

💡 Add up the three equal sides, then subtract from the total: leftover wire is just a tidy decimal subtraction you already know!

Variant 8 answer: 2.84 m

Using a $5\ \text{m}$ length of wire without overlapping, you bent it to make one equilateral triangle like the one shown. How many meters of wire are left over?

(Figure: one equilateral triangle, with one side labeled $0.72\ \text{m}$ .)

Show solution

Understand

A 5 m piece of wire is bent (no overlap) into one equilateral triangle whose side is 0.72 m. I need to find how much wire is left over after making the triangle.

Givens

Total wire length is 5 m.
The shape made is an equilateral triangle (all three sides equal).
Each side of the triangle is 0.72 m.
No wire overlaps when bending.

Unknowns

The length of wire left over, in meters.

Constraints

An equilateral triangle has exactly 3 equal sides.
Wire used equals the triangle's perimeter; leftover = total - perimeter.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram#8 Analyze the Units

Break the task into two small steps: first the perimeter (a side-length sum for an equilateral triangle), then a subtraction from the total wire. The figure shows one labeled side, and all sides are equal, so the perimeter is 3 copies of the side. Keeping the meters consistent guards against place-value slips with decimals.

Execute

#7 Identify Subproblems 5.NBT.B.7

An equilateral triangle has three equal sides of 0.72 m, so the wire used is the sum of the three sides.

0.72 + 0.72 + 0.72 = 0.72 \times 3 = 2.16 \text{ m}

Adding three equal decimals is the same as multiplying by 3; lining up the hundredths keeps the place values straight.

#7 Identify Subproblems 5.NBT.B.7

The leftover wire is the total length minus the wire used for the triangle.

5 - 2.16 = 2.84 \text{ m}

Subtract the used wire from the total, regrouping the decimals just like money amounts.

Answer: 2.84 m

Review

The triangle uses 2.16 m out of the 5 m wire. Check: 2.16 + 2.84 = 5 m, exactly the original wire, so 2.84 m left over is consistent.

Use Draw a Diagram (tool 1): sketch the wire as a number line, mark off three side-length hops for the triangle, and read the remaining length.

Standards · min grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the side by 3 for the perimeter and subtracting that from the total.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Treating the wire used as the triangle's perimeter (sum of side lengths).

💡 Add up the three equal sides, then subtract from the total: leftover wire is just a tidy decimal subtraction you already know!

Variant 9 answer: 3.3 m

Using a $6\ \text{m}$ length of wire without overlapping, you bent it to make one equilateral triangle like the one shown. How many meters of wire are left over?

(Figure: one equilateral triangle, with one side labeled $0.9\ \text{m}$ .)

Show solution

Understand

A 6 m piece of wire is bent (no overlap) into one equilateral triangle whose side is 0.9 m. I need to find how much wire is left over after making the triangle.

Givens

Total wire length is 6 m.
The shape made is an equilateral triangle (all three sides equal).
Each side of the triangle is 0.9 m.
No wire overlaps when bending.

Unknowns

The length of wire left over, in meters.

Constraints

An equilateral triangle has exactly 3 equal sides.
Wire used equals the triangle's perimeter; leftover = total - perimeter.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram#8 Analyze the Units

Break the task into two small steps: first the perimeter (a side-length sum for an equilateral triangle), then a subtraction from the total wire. The figure shows one labeled side, and all sides are equal, so the perimeter is 3 copies of the side. Keeping the meters consistent guards against place-value slips with decimals.

Execute

#7 Identify Subproblems 5.NBT.B.7

An equilateral triangle has three equal sides of 0.9 m, so the wire used is the sum of the three sides.

0.9 + 0.9 + 0.9 = 0.9 \times 3 = 2.7 \text{ m}

Adding three equal decimals is the same as multiplying by 3; lining up the hundredths keeps the place values straight.

#7 Identify Subproblems 5.NBT.B.7

The leftover wire is the total length minus the wire used for the triangle.

6 - 2.7 = 3.3 \text{ m}

Subtract the used wire from the total, regrouping the decimals just like money amounts.

Answer: 3.3 m

Review

The triangle uses 2.7 m out of the 6 m wire. Check: 2.7 + 3.3 = 6 m, exactly the original wire, so 3.3 m left over is consistent.

Use Draw a Diagram (tool 1): sketch the wire as a number line, mark off three side-length hops for the triangle, and read the remaining length.

Standards · min grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the side by 3 for the perimeter and subtracting that from the total.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Treating the wire used as the triangle's perimeter (sum of side lengths).

💡 Add up the three equal sides, then subtract from the total: leftover wire is just a tidy decimal subtraction you already know!

Variant 10 answer: 3.7 m

Using a $7\ \text{m}$ length of wire without overlapping, you bent it to make one equilateral triangle like the one shown. How many meters of wire are left over?

(Figure: one equilateral triangle, with one side labeled $1.1\ \text{m}$ .)

Show solution

Understand

A 7 m piece of wire is bent (no overlap) into one equilateral triangle whose side is 1.1 m. I need to find how much wire is left over after making the triangle.

Givens

Total wire length is 7 m.
The shape made is an equilateral triangle (all three sides equal).
Each side of the triangle is 1.1 m.
No wire overlaps when bending.

Unknowns

The length of wire left over, in meters.

Constraints

An equilateral triangle has exactly 3 equal sides.
Wire used equals the triangle's perimeter; leftover = total - perimeter.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram#8 Analyze the Units

Break the task into two small steps: first the perimeter (a side-length sum for an equilateral triangle), then a subtraction from the total wire. The figure shows one labeled side, and all sides are equal, so the perimeter is 3 copies of the side. Keeping the meters consistent guards against place-value slips with decimals.

Execute

#7 Identify Subproblems 5.NBT.B.7

An equilateral triangle has three equal sides of 1.1 m, so the wire used is the sum of the three sides.

1.1 + 1.1 + 1.1 = 1.1 \times 3 = 3.3 \text{ m}

Adding three equal decimals is the same as multiplying by 3; lining up the hundredths keeps the place values straight.

#7 Identify Subproblems 5.NBT.B.7

The leftover wire is the total length minus the wire used for the triangle.

7 - 3.3 = 3.7 \text{ m}

Subtract the used wire from the total, regrouping the decimals just like money amounts.

Answer: 3.7 m

Review

The triangle uses 3.3 m out of the 7 m wire. Check: 3.3 + 3.7 = 7 m, exactly the original wire, so 3.7 m left over is consistent.

Use Draw a Diagram (tool 1): sketch the wire as a number line, mark off three side-length hops for the triangle, and read the remaining length.

Standards · min grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the side by 3 for the perimeter and subtracting that from the total.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Treating the wire used as the triangle's perimeter (sum of side lengths).

💡 Add up the three equal sides, then subtract from the total: leftover wire is just a tidy decimal subtraction you already know!

Perimeter as decimal side sums minus overlaps · 10 practice problems

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