Question

The triangles shown are similar. What is the value of x?

Answer 1

Incomplete Question the complete question with the figure is below

The triangles shown are similar.

What is the value of x?

A. 12

B. 15

C. 20

D. 13

Answer:

The correct option is B. 15

Therefore the value of x is

`x=15\ unit`

Explanation:

Given:

AB = 5

BC = 3

AC = 4

PQ = x

QR = 9

RP = 12

ΔABC ~ ΔPQR

To Find:

x = ?

Solution:

ΔABC ~ ΔPQR .................Given

If two triangles are similar then their sides are in proportion.

`(AB)/(PQ) =(BC)/(QR)=(AC)/(PR) \textrm{corresponding sides of similar triangles are in proportion}\\`

Substituting the values we get

`(5)/(x) =(3)/(9)\\\\x=(45)/(3)=15\ unit`

Therefore the value of x is

`x=15\ unit`