Question

In given figure, PB and Qa are perpendiculars to segment AB. If PO=5 cm, QO=7 cm and Area $△POB=150{cm}^2$ find the area of $△QOA$.

Answer 1

In $△OAQ$ and $△OBP$, we have

$\angle A=\angle B$ [Each equal to ${90}^{\circ }$]

$\angle AOQ=\angle BOP$

So, by AA-criterion of similarity, we have

$△AOQ\sim △BOP$

$\Rightarrow$ $\frac{Area\left(△AOQ\right)}{Area\left(BOP\right)}=\frac{{OQ}^2}{{OP}^2}$

$\Rightarrow$ $\frac{Area\left(△AOQ\right)}{150}=\frac{7^2}{5^2}$

$\Rightarrow$ $Area\left(△AOQ\right)=\frac{49}{25}\times 150{cm}^2=294{cm}^2$