In given figure, ST || RQ, PS = 3 cm and SR = 4 cm. Find the ratio of the area of ∆PST to the area of ∆PRQ.

We have the triangle,

Given that:

ST || RQ

PS = 3 cm

SR = 4 cm

To find ratio of area of ∆PST and area of ∆PRQ, we need to prove ∆PST ∼ ∆PRQ.

To Prove: ∆PST ∼ ∆PRQ

Proof:

In ∆PST & ∆PRQ,

∠1 = ∠2 [∵ ST || RQ]

∠TPS = ∠QPR [∵ they are common angles of the triangles]

By AA-similarity of triangle property,

∆PST ∼ ∆PRQ

When two triangles are similar, then the ratio of areas of these triangles is equal to the ratio of the squares of their corresponding sides.

⇒

⇒

⇒

⇒

Hence, required ratio is 9:49.