Question

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

Answer 1

In triangle ABC and triangle ABD
<B = <B. ( Common )
<D = <A. ( 90°)
By AA similarity Triangle ABC similar to Triangle ABD.
Since the similar triangles possess the proportional corresponding sides

AB/BC = AD/AC
5 /13 = AD/ 12
5 × 12/13 = AD
4.61 cm = AD

Now Area of triangle ABC = 1/2 b × h = 1/2 × 5 ×12
= 30 cm sq....