In ( PQR ), point S lies on PR and point T lies on PQ such that ST is parallel to…

MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles

Problem

\triangle PQR

, point S lies on PR and point T lies on PQ such that ST is parallel to QR. (i) Prove that

\triangle PST

is similar to

\triangle PQR.

(ii) If

PS = 3\,\text{cm},\; SR = 6\,\text{cm}

and

PT = 4\,\text{cm},

find the length of TQ. (iii) Hence, find the ratio of the areas of

\triangle PST

and

\triangle PQR.