Question

In the given figure, S and T are points on the sides PQ and PR respectively of ∆PQR such that PT = 2 cm, TR = 4 cm and ST is parallel to QR. Find the ratio of the areas of ∆PST and ∆PQR.

Answer 1

Given: In ΔPQR, S and T are the points on the sides PQ and PR respectively such that PT = 2cm, TR = 4cm and ST is parallel to QR.

To find: Ratio of areas of ΔPST and ΔPQR

$$\begin{gathered} \mathrm{In}∆\mathrm{PST}\mathrm{and}∆\mathrm{PQR}, \\ \angle \mathrm{PST}=\angle \mathrm{Q}\left(\mathrm{Corresponding}\mathrm{angles}\right) \\ \angle \mathrm{P}=\angle \mathrm{P}\left(\mathrm{Common}\right) \\ \therefore ∆\mathrm{PST}~∆\mathrm{PQR}\left(\mathrm{AA}\hspace{0.17em}\mathrm{Similarity}\right) \end{gathered}$$

Now, we know that the areas of two similar triangles are in the ratio of the squares of the corresponding sides. Therefore,