Question

In the given figure, if $\angle A={90}^o,\angle B={90}^o,OB=4.5cm,OA=6cm$ and $AP=4cm$, then find $QB$.

Answer 1

In $\Delta AOP$ and $\Delta QOB$

$\angle A=\angle B=90°$

$\angle AOP=\angle QOB$ (vertically opposite angle)

$OA\ne OB$

$\therefore \Delta AOP$ and $\Delta QOB$ are similar $\Delta s$

$\therefore OA/OB=AP/QB$ (in similar Δs the ratio of corresponding sides are constants)

$QB=$ $AP\times \frac{OB}{OA}$

$QB=3cm$