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Math Help - [SOLVED] Polynomials to solve for area

  1. #1
    strafer
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    [SOLVED] Polynomials to solve for area

    A rectangular garden is 5 feet longer than twice its width. It has a sidewalk 3 feet wide on two of its sides. The area of the sidewalk is 213 square feet. Find the dimensions of the garden.


    2X +5 for length and x for width on the garden. x+ 3 and 2x+ 8 for the sidewalk.


    _____________ feet squared.

    Follow this example 80 x 120.

    The answer is 21 x 47 but i'm not sure what formula was used.

    Any help would be appreciated. Thanks
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Diagram

    [SOLVED] Polynomials to solve for area-capture.jpg
    So we end up with

    (w+3)(2w+8)-(w)(2w+5)=213

    2w^2+14w+24-2w^2-5w=213

    9w+24=213 \iff w=21

    so the length is

    l=2w+5=2(21)+5=47

    so w=21 and l=47
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  3. #3
    Senior Member Twig's Avatar
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    confused

    Im confused, doesnt he say that the SIDEWALK has an area of 213, not the sidewalk inlcluding the garden?
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