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Math Help - Dimensions of Dog Pen

  1. #1
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    Smile Dimensions of Dog Pen

    You wish to build a rectangular pen for your dog with 24 yards of fence. What are the dimensions (length and width) of the pen that will allow for maximum room to roam?

    Is there a way to solve this question without using a graphing calculator or calculus?

    Our teacher used a graphing calculator and found the maximum point to be (6,36) where the number 6 = the length and 36 = the width wirtten (L, W).

    That's find and dandy but how does answer this question without a calculator and without calculus?

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  2. #2
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    Quote Originally Posted by magentarita View Post
    You wish to build a rectangular pen for your dog with 24 yards of fence. What are the dimensions (length and width) of the pen that will allow for maximum room to roam?

    Is there a way to solve this question without using a graphing calculator or calculus?

    Our teacher used a graphing calculator and found the maximum point to be (6,36) where the number 6 = the length and 36 = the width wirtten (L, W).

    That's find and dandy but how does answer this question without a calculator and without calculus?
    Yes there is another way to solve this by making perfect square (completing the square)

    Let length of rectangular pen is x
    and width of rectangular pen is y.

    Perimeter P = 2x + 2y.

    \Rightarrow \; 24 = 2x + 2y

    \Rightarrow \; 12 = x + y

    \Rightarrow \; \boxed {\;y = 12 - x \;}

    Now Area A= x \times y

    A= x(12-x)

    = -x^2+12x

    A= -(x-6)^2+36

    So, the maximum area is 36 m^2 when x = 6 m, so that y = 12 - 6 = 6 m.
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  3. #3
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    Smile I knew it....

    Quote Originally Posted by Shyam View Post
    Yes there is another way to solve this by making perfect square (completing the square)

    Let length of rectangular pen is x
    and width of rectangular pen is y.

    Perimeter P = 2x + 2y.

    \Rightarrow \; 24 = 2x + 2y

    \Rightarrow \; 12 = x + y

    \Rightarrow \; \boxed {\;y = 12 - x \;}

    Now Area A= x \times y

    A= x(12-x)

    = -x^2+12x

    A= -(x-6)^2+36

    So, the maximum area is 36 m^2 when x = 6 m, so that y = 12 - 6 = 6 m.
    I knew there was another way.

    Thanks
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