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26 November, 14:35

If two opposite sides of a square are increased by 14 meters and the other sides are decreased by 7 meters, the area of the rectangle that is formed is 72 square meters. find the area of the original square.

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  1. 26 November, 15:03
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    Let us call that the original side of the square is called "s".

    So the new dimensions are:

    (s - 14) and (s - 7)

    The formula for area of rectangle is:

    A = l * w

    therefore:

    72 = (s - 14) * (s - 7)

    s^2 - 7s - 14s + 98 = 72

    s^2 - 21s = - 26

    Completing the square:

    s^2 - 21s + 110.25 = - 26 + 110.25

    (s - 10.5) ^2 = 84.25

    s = 10.5 ± 9.18

    s = 1.32, 19.68

    s must be bigger than 14, so the correct side of the square is:

    s = 19.68 m

    So the area of the original square is:

    A = s^2 = (19.68 m) ^2

    A = 387.3 square meters
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