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