Question

An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

Answer 1

Let the sides of an isosceles triangle be a = 12 cm, b = 12 cm, c = x cm

Since the perimeter of the triangle = 30 cm

∴ 12 cm + 12 cm + x cm = 30 cm

⇒ x = (30 − 24) = 6

Now, semi-perimeter, s = `30/2` cm = 15 cm

∴ Area of the triangle = `sqrt(s(s - a)(s - b)(s - c))`

= `sqrt(15(15-12)(15-12)(15-6))  cm^2`

= `sqrt(15 xx 3 xx 3 xx 9)  cm^2`

=  `sqrt(15 xx 3 xx 3 xx 3 xx 3 xx 3)  cm^2`

= `sqrt(3^2 xx 3^2 xx 3 xx 5)  cm^2`

= `3 xx 3 xx sqrt(3 xx 5)  cm^2`

= `9sqrt15  cm^2`

Thus, the required area of the triangle is `9sqrt15  cm^2`.