Question

It is given that ΔABC ~ ΔPQR, with `(BC)/(QR) = 1/3`. Then, `(ar(PRQ))/(ar(BCA))` is equal to ______.

Options

• 9

• 3

• `1/3`

• `1/9`

Answer 1

It is given that ΔABC ~ ΔPQR, with `(BC)/(QR) = 1/3`. Then, `(ar(PRQ))/(ar(BCA))` is equal to 9.

Explanation:

Given, ∆ABC ~ ∆QR and `(BC)/(QR) = 1/3`

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

∴ `(ar(∆PRQ))/(ar(∆BCA)) = (QR)^2/(BC)^2 = ((QR)/(BC))^2`

= `(3/1)^2`

= `9/1`

= 9