Question

In the figure below, triangle ABC is similar to triangle PQR, as shown below:

what is the length of side PQ?

A) 18

B) 4

C) 32

D) 6​

Answer 1

Answer: Option A

`PQ=18`

Explanation:

Two triangles are similar if the length of their sides is proportional.

In this case we have the triangle ∆ABC and ∆PQR so for the sides of the triangles they are proportional it must be fulfilled that:

`(AB)/(PQ)=(BC)/(QR)=(AC)/(PR)`

In this case we know that:

`BC=8`

`QR=24`

`AB=6`

Therefore

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

`(8)/(24)=(6)/(PQ)`

`PQ=6*(24)/(8)`

`PQ=18`

Answer 2

So, Option A is correct.

Explanation:

If the triangles are similar, then the sides are proportional

If triangle ABC is similar to triangle PQR

then sides

AB/PQ = BC/QR = AC/PR

We need to find PQ

We are given AB = 6, BC =8 and QR=24

AB/PQ = BC/QR

Putting values:

6/PQ = 8/24

Cross multiplying:

6*24 = 8*PQ

144/8 = PQ

=> PQ = 18

So, Option A is correct.