Question

If ∆ABC ~ ∆QRP, `(ar(ABC))/(ar(PQR)) = 9/4`, AB = 18 cm and BC = 15 cm, then PR is equal to ______.

Options

• 10 cm

• 12 cm

• `20/3` cm

• 8 cm

Answer 1

If ∆ABC ~ ∆QRP, `(ar(ABC))/(ar(PQR)) = 9/4`, AB = 18 cm and BC = 15 cm, then PR is equal to 10 cm.

Explanation:

Given, ∆ABC ~ ∆QRP, AB = 18 cm and BC = 15 cm

We know that, the ratio of the area of two similar triangles is equal to the ratio of square of their corresponding sides.

∴ `(ar(∆ABC))/(ar(∆QRP)) = (BC)^2/(RP)^2` 

But, `(ar(∆ABC))/(ar(∆PQR)) = 9/4`  .....[Given]

⇒ `(15)^2/(RP)^2 = 9/4`  .....[∵ BC = 15 cm, given]

⇒ `(RP)^2 = (225 xx 4)/9` = 100

∴ RP = 10 cm