Question

Given $\Delta ABC$ $\sim$ $\Delta PQR$, if $\frac{AB}{PQ}=\frac{1}{3}$ then find $\frac{ar\Delta ABC}{ar\Delta PQR}$.

Answer 1

$\Rightarrow$ $△ABC\sim △PQR$ [ Given ]

$\Rightarrow$ $\frac{AB}{PQ}=\frac{1}{3}$ [ Given ]

We know that, the ratio of areas of two similar triangles is proportional to the squares of the corresponding sides of both the triangles.

$\therefore$ $\frac{ar\left(△ABC\right)}{ar\left(△PQR\right)}={\left(\frac{AB}{PQ}\right)}^2$

$\Rightarrow$ $\frac{ar\left(△ABC\right)}{ar\left(△PQR\right)}={\left(\frac{1}{3}\right)}^2$

$\therefore$ $\frac{ar\left(△ABC\right)}{ar\left(△PQR\right)}=\frac{1}{9}$