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Math Help - Word problem with factoring

  1. #1
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    Word problem with factoring

    I can't seem to figure out this word problem that involves factoring. Here is the question and what I have so far:

    "The side of a square equals the width of a rectangle. The length of the rectangle is 6cm longer than its width. The sum of the areas is 176cm^2. Find the length of the side of the square."

    I'm not sure whether there are two separate equations in this equation.

    s = side of square
    w = width of rectangle
    area of square = (w)(length)
    w = s

    length of rectangle = ( w + 6)
    area of rectangle = w(w+6)

    I've tried pull all in a single equation which isn't. Any advice on how to solve this?
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  2. #2
    Super Member TheChaz's Avatar
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    Re: Word problem with factoring

    There is a square consructed on the (short) side of a rectangle
    The area of the square is w*w = w^2.
    The area of the rectangle is w*(w + 6) = w^2 + 6w.
    The sum of these areas is 176.
    (w^2) + (w^2 + 6w) = 176
    2w^2 - 6w - 176 = 0
    w^2 - 3w - 88 = 0
    etc.
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  3. #3
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    e^(i*pi)'s Avatar
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    Re: Word problem with factoring

    You have the area of a rectangle correct. You also know the area of the square is w^2

    You are told the sum of their areas is 176cm^2 which is the same as w^2 + w(w+6)=176

    Simplify, solve and discard and solutions less then 0.
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  4. #4
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    Re: Word problem with factoring

    Thanks for the help. This is what I finished with:

    (w+11)(w-8)

    8 = the length of the side
    Last edited by Robert12; July 27th 2011 at 12:43 PM.
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  5. #5
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    e^(i*pi)'s Avatar
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    Re: Word problem with factoring

    Yep, but don't forget your units: 8\text{ cm}
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