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Math Help - Length of sides of a rectangle

  1. #1
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    Length of sides of a rectangle

    If the perimeter of a rectangular garden plot is 34feet and its area is 60square feet, what is the length of each of the longer sides?

    I know area = l*w and then common sense tells me 12*5...but I always get the wrong answer setting up the problem.
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  2. #2
    Member Glaysher's Avatar
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    Quote Originally Posted by thecapaccino View Post
    If the perimeter of a rectangular garden plot is 34feet and its area is 60square feet, what is the length of each of the longer sides?

    I know area = l*w and then common sense tells me 12*5...but I always get the wrong answer setting up the problem.
    Let length = l and width = w

    Then perimeter = 2l + 2w and area = lw

    So 2l + 2w = 34 and lw = 60

    l = 60/w

    2(60/w) + 2w = 34

    120/w + 2w = 34

    120 + 2w^2 = 34w

    2w^2 - 34w + 120 = 0

    w^2 - 17w + 60 = 0

    (w - 12)(w - 5) =0

    w = 12 or w = 5

    If w = 5 then l = 60/w = 60/5 = 12

    If w = 12 then l = 60/w = 60/12 = 5

    So longest side is 12
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