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

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.

.

Answer 2

Step-by-step explanation:

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△PQRarea△PST=PR2PT2

area△PQRarea△PST=(PT+TR)242

area△PQRarea△PST=(4+4)216=8216=6416=41

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

1:4.

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