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