Question

In given figure, $ST||RQ,PS=3cm$ and $SR=4cm$. Find the ratio of the area of $△PST$ to the area of $△PQR.$

Answer 1

$ST\parallel RQ,PS=3cm,SR=4cm$

$△PST$ and $△PQR$ are equilateral $△$.

$\therefore \frac{ar\left(△PST\right)}{ar\left(△PQR\right)}=\frac{\frac{\sqrt{3}}{4}{a}^2}{\frac{\sqrt{3}}{4}{A}^2}=\frac{3^2}{(4+3{)}^2}$

$\frac{ar\left(△PST\right)}{ar\left(△PQR\right)}=\frac{9}{49}=9:49$