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Math Help - Perimeter help?

  1. #1
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    Exclamation Perimeter help?

    Hello!
    I am trying to figure out this problem

    A field is to be marked off in the shape of a rectangle of area 144 square feet.

    a. Write an expression for the perimeter, P, as a function of the length x

    for this, so far i know that the perimeter is 2l + 2w so how would i set this up?


    b. Use a calculator to approximate the dimensions for which the perimeter is a minimum ( I don't understand what this means)



    thanks for helping! ;D
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  2. #2
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    For a) you are asked to set up a set of simultaneous equations so that you get a function in terms of JUST the length...

    If x is the length and y is the width, then

    A = xy and P = 2x + 2y.

    Since A = 144\,\textrm{ft}^2, that means

    144 = xy

    y = \frac{144}{x}.


    So P = 2x + 2\left(\frac{144}{x}\right)

    P = 2x + \frac{288}{x}.


    b) I suppose you are asked to generate a list which gives you the perimeter for a number of x values. Otherwise you would be expected to use Calculus...
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  3. #3
    Junior Member bondesan's Avatar
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    You know that P = 2L + 2W, right?

    The exercise asks you to express P as a function of the lenght L. You know that the area of the rectangle is 144, therefore W.L = 144. If you put W = 144/L, you can express P as P = 2L + 288/L.

    Next, use your calculator to play with the function. Try some numbers and see if you can find one L that minimizes the value of P. I suggest you make a table with the values of L and the correspondent value of P.
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  4. #4
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    :O inteseresting! thank you!
    and for b) this is for my AP calc summer assignment... what would i need from calc to solve it? :S
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  5. #5
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    thank you so much!!
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