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