calculus

Find the length and width of a rectangle with maximum area that has a perimeter of (7P) units.


units (smaller value)

units (larger value)

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asked by Sam
  1. area=Lw
    perimeter=2L+2W

    area=LW
    7P=2L+2W
    L=7P/2-W

    area=W(7P/2-W)
    d area/dw=0=7P/2-2W

    W=7P/4
    then L=7P/2-7P/4=7P/4

    areamax=Lw=7P/4 ^2=49P^2/16

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