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26 November, 05:37

The hypotenuse of a right triangle is 7 inches longer than the base and 14 inches longer than the height. the permeter of the triangle is 84 inches. find its area

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  1. 26 November, 06:40
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    To determine the area of a triangle, we calculate one half of the product of the base and the height of the triangle so we need data on its base and its height. We are given the following:

    Hypotenuse = 7 + base = 14 + height

    Perimeter = 84 inches

    The perimeter of the triangle is equal to the sum of the three sides of the triangle which are the height, base and hypotenuse. So,

    Perimeter = height + base + hypotenuse = 84

    We let x = height and y = base. We calculate area as follows:

    84 = x + y + (7 + y)

    77 = x + 2y

    x = 77 - 2y

    Hypotenuse is related to the other sides by the Pythagorean theorem.

    Hypotenuse^2 = (x^2 + y^2)

    (14 + x) ^2 = x^2 + y^2

    (14 + (77-2y)) ^2 = (77-2y) ^2 + y^2

    (91-2y) ^2 = (77-2y) ^2 + y^2

    Solving for y and x

    y = 28

    x = 21

    Area = (28) (21) / 2 = 294 square inches
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