Posted by casidhe on Friday, April 20, 2012 at 10:17pm.
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  Reiny, Friday, April 20, 2012 at 11:03pm
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