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Math Help - largest area

  1. #1
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    Question largest area

    I need your help for this problem: Demonstate that in all
    rectangles which have the same compass the qudrate has the biggest area. I am waiting your answer now. Thanks
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  2. #2
    MHF Contributor
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    Quote Originally Posted by blertta View Post
    I need your help for this problem: Demonstate that in all
    rectangles which have the same compass the qudrate has the biggest area. I am waiting your answer now. Thanks
    Is this Calculus? Let me assume I can use Calculus.

    I understand that you mean, "Demonstate that in all rectangles that have the same perimeters, the square has the biggest area."

    Perimeter, P = 2(L +w) ---------(1)
    Area, A = w*L ---------------(2)

    From (1),
    L +w = P/2
    L = P/2 -w

    So,
    A = w(P/2 -w)
    A = (P/2)w -w^2
    Differentiate both sides with respect to w,
    dA/dw = P/2 -2w
    Set that to zero,
    0 = P/2 -2w
    2w = P/2
    4w = P ----------***

    Substitute that into (1),
    P = 2(L +w)
    4w = 2L +2w
    4w -2w = 2L
    2w = 2L
    L = w ---------meaning, length = width, which is a square.

    Therefore, the rectangle that is a square has the biggest area.
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