Question

In fig., 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, be AA-criterion of similarly, we have

$△$OAQ = $△$OBP

$\Rightarrow$ $\frac{area\left(△AOQ\right)}{area\left(△BOP\right)}=\frac{O{Q}^2}{O{P}^2}$

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

$\Rightarrow$ Area ($△AOQ)=\frac{49}{25}\times 150c{m}^2=294c{m}^2$