Question

Find the missing side length,x.

Answer 1

x = 12

Explanation:

In ΔABC ≈ ΔQRS , the squiggly line indicates that the triangles are similar meaning that the ratios of the corresponding side lengths are the same.

This means that
`(AB)/(QR) =(BC)/(RS) =(CA)/(SQ)`

Here, we are given the side lengths of AB, BC, RQ and we are asked to find the length of x or RS.

We can do so by setting a proportion, and then solving for x.

We've already found out that
`(AB)/(QR) =(BC)/(RS)`

So we can plug in the given values and solve for x

Given :

• AB = 6
• BC = 8
• QR = 9
• RS = x

`(AB)/(QR) =(BC)/(RS)`

==> plug in given values

`(6)/(9) =(8)/(x)`

==> cross multiply

6x = 72

==> divide both sides by 6

x = 12

We can check our answer by checking to see if the corresponding sides have similar ratios.

6/9 = 2/3 ✓

8/12 = 2/3 ✓