Geometry & Figures

Problem

Dashed edges in a sketch are hidden

A rectangular prism is drawn as a cabinet sketch. The three edges meeting at one corner measure ○ cm, 4 cm, and 7 cm. The edges you cannot see are drawn as dashed lines, and there is exactly one dashed edge of each length. Those three hidden edges add up to 16 cm. We need the value of ○.
○ cm 4 cm 7 cm
Geometry
Your answer
How to solve
Strategy Work Backwards — We know the finished total (16 cm) and want to recover one missing part, so working backwards from the total fits perfectly. First we use spatial visualization to see which edges are hidden — in a cabinet sketch exactly one edge of each length is dashed — so the hidden sum is just ○ + 4 + 7. Then we subtract the known parts from 16 to find ○. This stays arithmetic-only, so no algebra is needed.
1STEP 1

See which edges are hidden

The dashed edges are the three hiding behind the box: one unknown, one 4 cm and one 7 cm.

2STEP 2

Write the total of the hidden edges

Add up the three hidden edge lengths and set the sum equal to the given 16 cm.

○ + 4 + 7 = 16
3STEP 3

Combine the known parts

The two known hidden edges are 4 cm and 7 cm, which total 11 cm.

4 + 7 = 11
4STEP 4

Work backwards to find the unknown edge

Since the three hidden edges total 16 cm and the two known ones total 11 cm, the remaining edge ○ is 16 − 11.

○ = 16 - 11 = 5
Answer
5 cm
Check the answer by adding the three hidden edges forward: 5 + 4 + 7 = 16 cm, which matches the given total. The answer is a length in centimeters, and 5 cm sits sensibly between the other two edge lengths (4 cm and 7 cm).
Takeaway

The dashed edges are the ones hiding behind the box; add the lengths you know, then subtract from the total to uncover the missing one.

  • See which edges are hidden
  • Write the total of the hidden edges
  • Combine the known parts
  • Work backwards to find the unknown edge
Where next?
Another one like thissuggested

▶ Practice — 12 problems