Question

In the PQR, S and T are points on sides PQ and PR respectively such that

ST∥QR. If PT = 1 cm; PS=1.5 cm and SQ=3 cm, then find RT
​

Answer 1

Given:

ST∥QR

PT= 4 cm

TR = 4cm

In △PST and △PQR,

∠SPT=∠QPR(Common)

∠PST=∠PQR (Corresponding angles)

△PST∼△PQR(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.

area△PQR

area△PST

=

PR

2

PT

2

area△PQR

area△PST

=

(PT+TR)

2

4

2

area△PQR

area△PST

=

(4+4)

2

16

=

8

2

16

=

64

16

=

4

1

Thus, the ratio of the areas of △PST and △PQR is

1:

: