Question

Instructions: Find the missing segment in the image below.

? =
Find the Missing Segment
36
21
35

Answer 1

Proportional Triangles

Notice how there are two triangles shown in the image: a bigger one and a smaller one.

The smaller one has two given side lengths: 21 and 35.

The bigger one has two given side lengths as well: 36 and 35+x, x being the missing segment.

These side lengths are proportional, meaning we can write this about corresponding segments on the two triangles:

`(21)/(36)=(35)/(35+x)`

⇒ First, cross-multiply:

`21(35+x)=35*36\\735+21x=1260`

⇒ Combine like terms:

`21x=1260-735\\21x=525\\x=25`

Thus, the missing segment is 25.