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21 July, 15:27

The length of a rectangular room is one less than twice the width. The area of the room is 28 square feet. Find the dimensions of the room.

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Answers (2)
  1. 21 July, 15:34
    0
    The first step to solve this problem is to represent variables for the width and the length:

    Let w = width of the rectangle

    2w - 1 = length of the rectangle

    The formula to compute for the area of the rectangle is:

    A = LW

    Substituting the values and variables to the formula:

    28 = w (2w - 1)

    2w^2 - w = 28

    2w^2 - w - 28 = 0

    Solve the quadratic equation:

    (2w + 7) (w - 4) = 0

    w = - 7/2 or w = 4

    You cannot use the - 7/2 because there is no negative measurement.

    W = 4 feet

    L = 2 (4) - 1 = 7 feet

    Therefore the dimension of the rectangle is 4 feet by 7 feet.
  2. 21 July, 15:46
    0
    Equation: x (2x-1) = 28

    Create a quadratic equation: 2x^2 - x=28

    2x^2 - x-28=0

    Find roots: plug into quadratic formula, x=4 or x=-7/2

    Since x cannot be negative, x=4

    Plug into original equation to find the width, width=7

    Check: Plug into original equation or just multiply the two using the formula for area

    7*4=28

    28=28

    Length is 4 ft, width is 7 feet
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