Question

In the triangle PQR, S is the midpoint of QR. X is any point on PR. T is the point on QR such that PT || SX. If the arca of triangle PQR is 5.8 sq. cm. then the area of triangle RTX is

Answer 1

Given:

ST || QR

PT= 4 cm

TR = 4cm

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(∆PST) /ar(∆PQR)= (PT)²/(PR)²

ar(∆PST) /ar(∆PQR)= 4²/(PT+TR)²

ar(∆PST) /ar(∆PQR)= 16/(4+4)²= 16/8²=16/64= 1/4

Thus, the ratio of the areas of ΔPST and ΔPQR is 1:4.