Algebra world problem

The length of a rectangle is 7 centimeters less than twice its width. Its area is 72 square meters. Find the dimensions of the rectangle.

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  1. width --- x
    length --- 2x-7

    x(2x-7) = 72
    2x^2 - 7x - 72 = 0
    (x-8)(2x+9) = 0
    x = 8 or x = -9/2, rejecting the negative width

    the rectangle is 8 by 9

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  2. Let l be 2x -7
    w = x

    A = lw
    72 = (2x-7)x
    72 = 2x^2 -7x
    2x^2 -7x -72 =0
    (2x+9)(x-8) = 0

    x -8 = 0

    x = 8
    l = 2x-7
    l = 2(8) -7
    l = 16-7= 9

    L = 9 m and w =8 m

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  3. Aren't the dimensions?

    width --- x
    length --- 2x-0.07

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    Ms. Sue
  4. good catch Ms Sue.

    so
    x(2x-.07) = 72
    2x^2 - .07x - 72 = 0
    x = (.07 ± √576.0049)/4
    = 6.017 or a negative

    width = 6.017
    length = 11.965

    check: area = 6.017(11.965) = 71.993 , not bad

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