Question

In a $△ABC$,$\angle ABC={90}^{\circ }$ and $BD$ is perpendicular to $AC$. If $BD=8$ cm and $AD=4$cm then find the length of $CD$?

Answer 1

Given:

$\angle ABC={90}^o,BD\perp AC$,

$BD=8$ and $AD=4$ as in diagram.

Let $\angle ACB=x$

$\Rightarrow \angle CBD=90-x$

$\Rightarrow \angle ABD=x$

$\Rightarrow \angle BAD=90-x$

$\Rightarrow \Delta ABC,\Delta ADB$ and $\Delta BDC$ are similar

$\Rightarrow \frac{BD}{CD}=\frac{AD}{DB}$

$\Rightarrow \frac{8}{CD}=\frac{4}{8}$

$\Rightarrow CD=\frac{8\times 8}{4}=16$cm.