Question

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

Answer 1

$<b><big>SOLUTION$

∆ABC is right - angled at A.

so, BC is definitely hypotenuse.

let AB is base and AC is altitude of ∆ABC.

given, AB = 5cm , BC = 13cm and AC = 12cm

now, area of triangle ∆ABC = 1/2 × base × altitude

= 1/2 × length of AB × length of AC

= 1/2 × 5cm × 12cm = 30 cm²

hence, area of ∆ABC = 30cm²

area of ∆ABC = 1/2 × length of AB × length of AC = 1/2 × length of BC × length of AD

=> 5cm × 12cm = 13cm × length of AD

=> 60/13 = length of AD

hence, length of AD = 60/13 cm