Question

The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.

Answer 1

The perimeter of isosceles triangle = 32cm
p of isosceles triangle = 2 * equal side + base
let length of equal side be 3x and base be 2x
then
2 * 3x + 2x = 32 cm
6x + 2x = 32cm
8x = 32 cm
x= 4 cm
length of equal side = 3*4= 12cm
length of base = 2*4=8cm
area of isosceles triangle=b*$\frac{1}{4}$ *√4$a^2$-$b^2$
= 8*$\frac{1}{4}$ √4*144-64
=2√512
=2*22.62
= 45.25${cm}^2$