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Math Help - perimeter / area verification problem

  1. #1
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    perimeter / area verification problem

    A rectangle is required to have an area of 4 square feet but it's dimensions may vary. If one side has a length x, express the perimeter p of the rectangle as a function of x.

    I think the answer is

    p = 2(2 + x)

    Can someone please verify?
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  2. #2
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    Quote Originally Posted by squidly View Post
    A rectangle is required to have an area of 4 square feet but it's dimensions may vary. If one side has a length x, express the perimeter p of the rectangle as a function of x.

    I think the answer is

    p = 2(2 + x)

    Can someone please verify?
    Let the length of the rectangle be x and the width be y.

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


    You're also told A = 4, so

    4 = xy

    y = \frac{4}{x}.


    Therefore

    P = 2x + 2\left(\frac{4}{x}\right)

    P = 2x + \frac{8}{x}.


    So no, your answer is not correct.
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  3. #3
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    Thanks for the correction. I just picked up a book and this problem was one of first exercises. The old solve equations with a few unknowns eluded me. Thank you kindly for the verification.
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