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Math Help - quadratic problem

  1. #1
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    Sep 2008
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    quadratic problem

    Hi, I'm having problems on how to setup this problem. Would appreciate any help.

    A gutter is to be made by folding up the edges of a strip of metal. If the metal is 12 in wide and the cross-sectional area of the gutter is to be 16 7/8 in sq, what are the width and depth of the gutter.

    I understand that the length of the one side is 12-2x, but I don't know how this helps me.

    Thanks
    Ryan
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, Ryan!

    A gutter is to be made by folding up the edges of a strip of metal.
    If the metal is 12 in wide and the cross-sectional area of the gutter is to be 16 7/8 in sq,
    what are the width and depth of the gutter?
    Code:
       This is the strip of metal before folding.
    
          : - - - - -12 - - - - - : 
          *-----*-----------*-----*
          :  x  :   12-2x   :  x  :
    
    
    
        This is the gutter after folding.
    
                *           *
                |           |
              x |           | x
                |           |
                *-----------*
                    12-2x

    The cross-sectional area is: . A \;=\;x(12-2x)

    We're told that this area will be: 16\frac{7}{8} \:=\:\frac{135}{8} inē.


    There is our equation . . . x(12-2x) \:=\:\frac{135}{8}

    Multiply by 8: . 8x(12-2x) \:=\:135 \quad\Rightarrow\quad 16x^2 - 96x + 135 \:=\:0

    Factor: . (4x-9)(4x-15) \:=\:0 \quad\Rightarrow\quad x \;=\;\frac{9}{4},\;\frac{15}{4}


    There are two solutions . . .

    . . . \begin{array}{|c|c|}\hline<br />
\text{Height} & \text{Width} \\<br />
x & 12-2x \\ \hline \hline<br />
2.25 & 7.5 \\ \hline \hline<br />
3.75 & 4.5 \\ \hline<br />
\end{array}

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  3. #3
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    Sep 2008
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    I was missing that the height = x. Thanks for the help!
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