Question

In given figure, $△ACB\sim △APQ$. If BC=8 cm, PQ=4 cm, BA=6.5 cm, AP=2.8 cm, find CA and AQ.

Answer 1

We have,
$△ACB\sim △APQ$

$\Rightarrow$ $\frac{AC}{AP}=\frac{CB}{PQ}=\frac{AB}{AQ}$

$\Rightarrow$ $\frac{AC}{AP}=\frac{CB}{PQ}$ and $\frac{CB}{PQ}=\frac{AB}{AQ}$

$\Rightarrow$ $\frac{AC}{2.8}=\frac{8}{4}$ and $\frac{8}{4}=\frac{6.5}{AQ}$

$\Rightarrow$ $\frac{AC}{2.8}=2$ and $\frac{6.5}{AQ}=2$

$\Rightarrow$ $AC=(2\times 2.8)cm=5.6cm$ and $AQ=\frac{6.5}{2}cm=3.25cm$