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Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540m. Find its area

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by shafi1987

pls i need it fast

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by shafi1987

pls i need it fast

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Perimeter of triangle is (12n + 17n + 25n) = 540 or 54n = 540 ==> n = 10. Hence sides of triangle are 120, 170, 250.

Area of triangle can be found by using formula Area = √[s(s-a)(s-b)(s-c)] where a, b, c are sides of the triangle and s = (a+b+c)/2.

Here s = (12+17+25)/2 = 54/2 = 27.

s-a = 27-12 = 15, s-b = 27-17 = 10, s-c = 27-25 = 2.

Hence Area = √(27x15x10x2) = √[(3x3x3)(3x5)(5x2)x2]

= √[(3x3)x(3x3)(5x5)(2x2)

= 3 x 3 x 5 x2 = 90 sqm

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Sides are in the ratio: