Question

Question 7

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

Answer 1

In right angle triangle BAC, AB = 5 cm and AC = 12 cm

Area of triangle = $\frac{1}{2}\times base\times height$
$=\frac{1}{2}\times AB\times AC$
$=\frac{1}{2}\times 5\times 12$
$=30c{m}^2$

Now, in $\Delta ABC,$

Area of triangle ABC
$=\frac{1}{2}\times BC\times AD$
$\Rightarrow 30=\frac{1}{2}\times 13\times AD$
$\Rightarrow AD=\frac{30\times 2}{13}=\frac{60}{13}cm=4.615cm$