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24 July, 18:08

If you have 50 feet of fence, what shape would yield the greatest area in yards?

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  1. 24 July, 19:41
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    Square

    Step-by-step explanation:

    Perimeter of a rectangle is

    P=2 (l+w)

    Where l is length and w is width

    Substituting 50 for P

    50=2 (l+w)

    25=l+w

    Making w the subject of formula then

    w=25-l

    Area is lw and substituting for w

    A=l (25-l) = -l²+25l

    A=-l²+25l

    Getting firat derivative of A with respect to l

    -2l+25=0

    l=25/2=12.5 yards

    Width will be 25-12.5=12.5 yards

    The dimensions of length and width are same hence the shape is square
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