An isosceles triangle has perimeter `30\ c m` and each of the equal sides of `12\ c mdot` Find the area of the triangle.

Options

A. `8sqrt15cm^2`
B. `7sqrt15cm^2`
C. `9sqrt15cm^2`
D. `4sqrt15cm^2`

Answer

C

Explanation

Here, Perimeter of the isosceles triangle `P = 30cm`

So, Semi-perimeter of the triangle, `s = 30/2 = 15cm`


Two sides of the triangle are `12cm`. So, `a=b = 12cm`

Third side, `c = P-a-b = 30-12-12 = 6cm`

Now, Area of the triangle, `A = sqrt(s(s-a)(s-b)(s-c))`(Herons formula)

`A = sqrt(15(3)(3)(9)) = 9sqrt15cm^2`