calculus

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Find the dimensions of the rectangle with area 256 square inches that has minimum perimeter, and then find the minimum perimeter.

Dimensions:

Minimum Perimeter:

  • calculus -

    length -- x
    width -- y
    xy = 256
    y = 256/x

    perimeter = 2x + 2y
    = 2x + 2(256/x) = 2x + 512/x
    d(perimeter)/dx = 2 - 512/x^2
    = 0 for a min of perimeter

    2 = 512/x^2
    x^2 = 256
    x = √256 = 16

    if x = 16, then y = 256/16 = 15
    perimeter = 2(16)=2(16) = 64

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