# 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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