Math

A rectangular lot is to be fenced using 80m of fencing. What is the maximum area and what are the dimensions of the lot?

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  1. P=Perimeter

    A=Area

    P=2a+2b

    80=2a+2b Divide both sides with 2

    40=a+b

    40-b=a

    a=40-b

    A=a*b

    A=(40-b)*b

    A=40b-b^2

    dA/dB=40-2b

    Function has maximum where first derivation=0

    and second derivation<0

    First derivation:

    dA/dB=40-2b=0

    40=2b Divide booths sides with 2

    20=b

    b=20m

    a=40-b=40-20=20m

    Second derivation= -2

    For a=20m and b=20m rectangle with maximum area is a square.

    A(max)=20*20=400m^2

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