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Math Help - Window Dimensions

  1. #1
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    Window Dimensions

    The area of a rectangular window is to be 306 square centimeters. If the length exceeds the width by 1 centimeter, what are the dimensions?
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  2. #2
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    The area of a rectangle is length (l) * width (w)

    l = w + 1

    (length is 1 more than width)

    We can now write the problem as this:

    306 = w(w + 1)
    306 = w^2 + w
    0 = w^2 + w - 306

    We can use the quadratic formula to find the solutions:

    0 = (-b +- sqrt(b^2 - 4ac))/2a

    The coefficient of w^2 is 1, so a = 1; the coefficient of w is 1, so b = 1; and c = -306.

    0 = (-1 +- sqrt(1^2 - 4(1)(-306)))/2(1)
    0 = (-1 +- sqrt(1 + 1225))/2
    0 = (-1 +- 35)/2

    This gives us 17 for one solution:

    (-1 + 35)/2
    34/2
    17

    and 18 for the other solution:

    (-1 - 35)/2
    -36/2
    -18

    Since the width cannot be negative, the width must be 17.

    l = w + 1
    l = 17 + 1
    l = 18

    The length is 18 cm and the width is 17 cm.
    Last edited by machi4velli; January 13th 2007 at 12:14 PM.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by symmetry View Post
    The area of a rectangular window is to be 306 square centimeters. If the length exceeds the width by 1 centimeter, what are the dimensions?
    If the length is x cm, then the width is x-1, so the area of the window is:

    x(x-1)=306.

    Solve this with the quadratic formula and you find x=-17 or x=18 are the
    roots the first is a non-physical result and so we discard it, leaving the length
    as 18 cm, and the width as 17 cm.

    Check 17*18=306, so the result is OK

    RonL
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  4. #4
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    ok

    Thank you both for your great help.
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