Question

Δ 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 Δ ABC. Also, find the length of AD. 

Answer 1

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

Area of triangle =1/2 x base x height 

= 1/2x AB x AC

= 1/2 x 5 x 12 = 30 cm²

Now, in Δ ABC,

Area of triangle ABC =1/2 x BC x AD

⇒ 30 = 1/2 x 13 x AD

⇒ AD = (30 x 2)/13

= 60/13 cm