Question

The perimeter of an isosceles triangle is 32 cm. If each equal side is `5/6` th of the base, find the area of the triangle.

Answer 1

The area of the isosceles triangle is 48 cm².

Let the base of the triangle be b.

Each equal side is `5/6`b.

Given perimeter equation:

`b + 2 xx 5/6b = 32`

`b + 10/6b = 32`

`16/6b = 32`

`b = (32 xx 6)/16 = 12` cm

Calculating equal sides:

`s = 5/6 xx 12 = 10` cm

Use Heron’s formula to find the area:

`s_p = (b + 2s)/2 = (12 + 2(10))/2 = 32/2 = 16` cm

`A = sqrt(s_p (s_p - b)(s_p - s)(s_p - s))`

`A = sqrt(16(16 - 12)(16 - 10)(16 - 10))`

`A = sqrt(16 xx 4 xx 6 xx 6)`

`A = sqrt2304`

= 48 cm²