Question

$\Delta ABC$ is a right-angle at $A$ $AD$ is perpendicular to $BC$ , $AB=5cm$ , $BC=13cm$ and $AC=12cm$ . Find the area of $\Delta ABC$ . Also , find the length of $AD$.

Answer 1

ln $\Delta sABD$ and $ABC$

$\Rightarrow \angle ABD=\angle ABC$ (common

$\angle ADB=\angle BAC={90}^0$

$\therefore \angle BAD=\angle ACB$ (sum of angles fo a $\Delta ={180}^0$)

$\angle ABD\sim \Delta CBA$

$\therefore \frac{AB}{CB}=\frac{BD}{BA}=\frac{AD}{CA}$

$\Rightarrow \frac{5}{13}=\frac{AD}{12}\Rightarrow AD=\frac{12\times 5}{13}=\frac{60}{13}cm$

In $ABC=\frac{1}{2}b.h=\frac{1}{2}\times 5\times 12=30c{m}^2$