Question

In figure, $\angle CAB={90}^{o}andAD\perp BC$. if AC =75 cm, AB=1 m and BD=1.25 m,find AD.

Answer 1

In $△BACand△$, we have
$\angle BAC=\angle BDA$ [Each equal to ${90}^o$]
and, $\angle B=\angle B$
So, by AA-criterion of similarity, we have
$△BAC\sim △BDA$
$\Rightarrow \frac{BA}{BD}=\frac{AC}{AD}$
$\Rightarrow \frac{100}{125}=\frac{75}{AD}$
$\Rightarrow AD=\frac{125\times 75}{100}cm=93.75cm$