Instructions: Find the missing segment in the image below. ? = Find the Missing Segment 36 21 35

Question

asked Oct 2, 2024 57.0k views

1 Answer

Sanah · Answer 1 · 2024-10-08T13:38:14+0000

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.