Question

$△ABC$ is right angled at $A$. $AD$ is perpendicular to $BC$. If $AB=5cm,BC=13cm$ and $AC=12cm$. Find the area of $△ABC$. Also find the length of $AD$.

Answer 1

Give that $△ABC$ right angled at A.

Base $AB=5cm$

Height $AC=12cm$

therefore,

Area of triangle $=\frac{1}{2}AB\times AC$

$=\frac{1}{2}\times 5\times 12$

$=30c{m}^2$

Now, consider

Base $BC=13cm$

Height $AD$

Area $=\frac{1}{2}BC\times AD$

$\Rightarrow 30=\frac{1}{2}\times 13\times AD$

$\Rightarrow AD=\frac{60}{13}$

$\Rightarrow AD=4.615cm$