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Very simple math question

  1. May 14, 2006 #1
    I am trying to remember how I would go about solving an equation like so.

    What is the smallest perimiter of a rectangle with area of 64 cm^2.

    I know I can use the graphing calculator.

    So I know there are two sides, x and 64 / x.

    If I try and graph x(64/x) I just get a straight line at 64. So how does one go about solving a question like this?

    Thank you.
     
  2. jcsd
  3. May 14, 2006 #2

    Hurkyl

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    Which is good -- you're graphing the area of your rectangle. It had better be a constant value!
     
  4. May 14, 2006 #3
    Lol, I understand why it is giving me that (because the x's cancel) which I am sure you know.

    If I had the inverse of this question, something like. The perimiter of a rectangle is 100 cm. What is the largest area it can have?

    I would go

    Side 1: x
    Side 2: 50 - x

    Graphing: x(50-x) thus at the maximum, x = 25.
    Therby making the other side 25 as well, for a maximum area of 625 cm.
     
  5. May 14, 2006 #4

    dav2008

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    Well if you're trying to minimize perimeter in your original problem, what should you be graphing?
     
  6. May 14, 2006 #5

    Hurkyl

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    When looking for the rectangle with the largest area, why do you do those steps?
     
  7. May 14, 2006 #6
    wait a minute.... If

    Side 1: x
    Side 2: 64 / x

    To find the smallest area couldnt I graph 2(x) + 2(64 / x) and find the smallest perimiter?
     
  8. May 14, 2006 #7
    Thus graphing, gives me an x value of 8 and a perimiter of 32.
     
  9. May 14, 2006 #8

    Hurkyl

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    That sounds good.
     
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