Question

In Fig., S and T are points on the sides PQ and PR respectively of A PQR such that PT = 2 cm, TR = 4 cm and ST is parallel to QR. Find the ratio of the areas of △PST and △ PQR.

Answer 1

Given

ST || QR, TR = 4 cm and PT = 2 cm. 

So,

PR = 6 cm. 

In ΔPST and ΔPQR,

∠PST = ∠PQR [corresponding angles]

∠PTS = ∠PRQ [corresponding angles]

∠P = ∠P [common angle]

We know that AAA similarity criterion states that in two triangles, if corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar. 

∴ ΔPST ~ ΔPQR 

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

∴ ar (ΔPST): ar (ΔPQR) = 1: 9