Question

∆ ABC is right angled at A (Fig 9.16). AD is perpendicular to BC. If AB = $5$ cm, BC = $13$ cm and AC = $12$ cm, Find the area of ∆ ABC. Also find the length of AD.

Answer 1

$Area= \frac{1}{2}\times Base \times Height$

$=\frac{1}{2}\times 5\times 12=30\; cm^2$

Also, area of triangle = $\frac{1}{2}\times AD\times BC$

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

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

$AD=4.6\;cm$