Question

. In the triangle PQR below,
- S and T are 2 points on the sides RP and RQ respectively such that ST is parallel to PQ.
- The ratio of RT to TQ is 1:2.
The area of ΔRST = 100 sq. units.
What is the area of PQTS?

Answer 1

Answer:

The answer will be 800 cm².

Step-by-step explanation:

Using Basic Proportionality Theorem,It can be proved that the Triangle RPQ And Triangle RST are similar.

As RT:TQ=1x:2x

=>RQ=RT+TQ=1x+2x=3x

=>RT:RQ=1:3

Area of RPQ and RST are in the ratio=1²:3²

=1:9

The area of RST is 100 cm².

Let the area of RPQ be x cm².

1:9=100:x

=>x=900cm².

Thus the area of RPQ is 900 cm².

Area of PQST=Area of RPQ-Area of RST

=900-100

=800 cm².

Hope it helps you.☺️