Question

Area of an isosceles triangle is 48 cm². If the altitudes corresponding to the base of the triangle is 8 cm, find the perimeter of the triangle.

Answer 1

Given, area of ΔABC = 48 cm² and altitude = 8 cm

∵ ΔABC is an isosceles triangle, where AB = AC

∴ Area of ΔABC = `1/2` × BC × AD = 48  ...[∵ Area of triangle = Base × Height]

⇒ 48 = `1/2` × BC × AD

⇒ `1/2` × BC × 8 = 48

⇒ BC = `(48 xx 2)/8`

BC = 12 cm

Now, in an isosceles triangle, BD = DC = 6 cm  ...[∵ AD ⊥ BC]

Applying Pythagoras theorem in right-angled ΔADB,

AB² = BD² + AD²

⇒ AB² = 6² + 8² = 36 + 64

⇒ AB² = 100

⇒ AB = 10 cm

Now, perimeter of triangle = AB + AC + BC

= AB + AB + BC  ...[∵ AB = AC]

= 10 + 10 + 12

= 32 cm