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Math Help - Need help with algebraic word problem

  1. #1
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    Need help with algebraic word problem

    Rain-Gutter Design:

    An open rectangular gutter is made by turning up the sides of a piece of metal 20 in. wide. The area of the cross-section of the gutter is 50 in^2. Find the depth of the gutter.

    So far this is what I have done:
    A= LW
    50 = L (20)
    L = A/W = 50/20 = 2.5 in

    Is this correct?
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  2. #2
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    rain gutter design

    posted by mcruz

    you have the right idea but are making a simple mistake.Express an equation in W and L equal to 20. You will then have two equations iin W and L.Solve and find W and LThen check so that givens are satisfied

    bjh
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  3. #3
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    Hello, mcruz65!

    An open rectangular gutter is made by turning up the sides of a piece of metal 20 in. wide.
    The area of the cross-section of the gutter is 50 inē.
    Find the depth of the gutter.
    Code:
          *         *
          |         |
        D |         | D
          |         |
          * - - - - *
               W

    The depth of the gutter is D.
    The width of the gutter is W.


    We have: . W + 2D \:=\:20 \quad\Rightarrow\quad W \:=\:20-2D .[1]


    The area is 50 inē: . DW \:=\:50 .[2]


    Substitute [1] into [2]: . D(20-2D) \:=\:50

    . . which simplifies to: . D^2 - 10D + 25 \:=\:0

    Factor: . (D-5)(d-5) \:=\:0

    Therefore: . D = 5


    The depth of the gutter is 5 inches.

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  4. #4
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    Thank you for your help!

    I really appreciate the help.
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  5. #5
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    yes but ya also need to find the depth
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