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The perimeter of a triangle is 170 ft and the sides are in the ratio of 25:14:12. Find the area of the triangle

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  1. 6 May, 11:51
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    using the ratio, the length of the sides are:

    25x + 14x + 12x = 170

    51x = 170

    x = 170 / 51

    x = 3 1/3

    The lengths of the sides are: 25 * 3 1/3 = 83 1/3 feet

    14 x 3 1/3 = 46 2/3 feet

    12 x 3 1/3 = 40 feet

    Using Heron's formula

    the semi perimeter (S) = 170/2 = 85 ft.

    The area of the triangle = SQRT (S * (S-83 1/3) * (S - 46 2/3) * (S-40))

    = SQRT (85 * (85-83 1/3) * (85 - 46 2/3) * (85-40)

    = SQRT (85 * 1 2/3 * 38 1/3 * 45)

    = SQRT (244374)

    = 494.34 square feet (round answer as needed).
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