Question

In a right-angled triangle ABC, if ∠B = 90°, AB - BC = 2 cm; AC - BC = 4 and its perimeter is 24 cm, find the area of the triangle.

Answer 1

Given, Perimeter of ΔABC = 24cm
⇒ AB + BC + AC = 24cm   ....(i)
AB - BC = 2cm    ....(ii)
AC - BC = 4cm   ....(iii)
Adding (ii) and (iii), we get
AB + AC - 2BC = 6cm
⇒ AB + AC = 6 + 2BC   ....(iv)
Substituing (iv) un (i), we get
6 + 2BC + BC = 24
⇒ 3BC = 18
⇒ BC = 6cm
⇒ AB = 2 + BC
= 2 + 6
= 8cm
∴ Area of right-angled ΔABC

= `(1)/(2) xx "BC" xx "AB"`

= `(1)/(2) xx 8 xx 6`
= 24cm².