Question

In a ΔPQR, S and T are points on the sides PQ and PR respectively, such that ST || QR. If PT = 2 cm and TR = 4 cm, find the ratio of the areas of ΔPST and ΔPQR.

Answer 1

Given, ST || QR, PT = 2 cm and TR = 4 cm

In ΔPST and ΔPQR,

∠SPT = ∠QPR   ...(Common)

∠PST = ∠PQR   ...(Corresponding angles)

∴ ΔPST ∼ ΔPQR   ...(By AA similarity criterion)

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

∴ `(ar (ΔPST))/(ar(ΔPQR)) = (PT^2)/(PR^2)`

= `2^2/(PT + TR)^2`

= `4/(2 + 4)^2`

= `4/36`

= `1/9`