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