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Math Help - Quick word problem

  1. #1
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    Quick word problem

    A rectangular area is enclosed by a fence and divided by another section of fence parallel to two of its sides. If the 600m of fence used encloses a maximum area, what are the dimensions of the enclosure?

    My work:

    2L + 3W = 600
    2L = 600 - 3W
    L = 300 - 1.5W
    A = LW
    A = (300 - 1.5W)W
    A = w(300 - 1.5W)
    Zeros: X=0, X= 200
    200/2 = 100
    Width: 100
    Length: 200

    Correct ?
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  2. #2
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    Hello, irishad!

    Thank you for showing your work!

    A silly arithmetical error at the very end . . .


    A rectangular area is enclosed by a fence and divided
    by another section of fence parallel to two of its sides.
    If the 600m of fence used encloses a maximum area,
    what are the dimensions of the enclosure?

    My work:

    2L + 3W \:= \:600\quad\Rightarrow\quad 2L \:= \:600 - 3W \quad\Rightarrow\quad L \:= \:300 - 1.5W

    A \:= \:LW \;=\;(300 - 1.5W)W \;=\;W(300 - 1.5W)

    Zeros: . x=0,\;x= 200\quad\Rightarrow\quad \frac{200}{2}\:=\:100

    .Width: . 100
    Length: . 200 \quad {\color{red}\leftarrow\quad oops!}
    The length is: . L \,=\,150

    But your reasoning (and the rest of your work) is absolutely correct.

    . . Good work!

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  3. #3
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    How is the length 150 ? :S
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  4. #4
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    Hello, irishad!

    How is the length 150 ?
    I have a question . . . Where in the world did you get 200 ?


    You had:. L \:=\:300 - 1.5W

    Then you found: . W \,=\,100

    Therefore . . .

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