Question

In the given figure, $PB$ and $QA$ are perpendicular to line segment $AB$. If $PO=7cm$, $QO=12cm$, and area of $\Delta POB=245c{m}^2$, find the area of $\Delta QOA$.



[2 marks]

• A. $120c{m}^2$
• B. $360c{m}^2$
• C. $480c{m}^2$
• D. $720c{m}^2$

Answer 1

The correct option is D $720c{m}^2$

In $\Delta POB$ and $\Delta QOA$,
$\angle PBO=\angle QAO...\left(\text{equal to}90°\right)$
$\angle POB=\angle QOA...$ (vertically opposite angles)

$\Delta POB\sim \Delta QOA...$ (by AA)
$\frac{\text{Area of}\Delta POB}{\text{Area of}\Delta QOA}={\left(\frac{PO}{QO}\right)}^2$
$\frac{245}{\text{Area of}\Delta QOA}={\left(\frac{7}{12}\right)}^2$
$\text{Area of}\Delta QOA=\frac{245\times 144}{49}$
$\text{Area of}\Delta QOA=720c{m}^2$