Question

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

Answer 1

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

Area of triangle$$=\dfrac{1}{2}\times$$base$$\times$$height$$=\dfrac{1}{2}\times$$AB$$\times$$AC

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

Now, in $$\Delta$$ABC,

Area of triangle ABC$$=\dfrac{1}{2}\times$$BC$$\times$$AD

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

$$\Rightarrow$$ AD$$=\dfrac{30\times 2}{13}=\dfrac{60}{13}$$cm.