Question

The base of an isosceles triangle is 24 cm and its area is 192 sq. cm. Find its perimeter.

Answer 1

It is given that

Area = 192 sq.cm

base = 24 cm

Knowing the length of the equal side, a and base, b of an isosceles triangle, the area can be calculated using the formula,

A = `1/4 xx b xx sqrt (4a^2 - b^2`     

Let 'a' be the length of an equal side.

Area = `1/4 xx b xx sqrt(4a^2 - b^2)`   

192 = `1/4 xx 24 xx sqrt(4a^2 - 576)` 

192 = `6 sqrt(4a^2 - 576)` 

`sqrt(4a^2 - 576` = 32

4a² – 576 = (32)²

4a² – 576 = 1024

4a² = 1024 + 576

4a² = 1600

a = 20 cm

Hence, perimeter = 20 + 20 + 24

= 64 cm