Asked by casidhe
Find the dimensions of the rectangle with area 256 square inches that has minimum perimeter, and then find the minimum perimeter.
Dimensions:
Minimum Perimeter:
Dimensions:
Minimum Perimeter:
Answers
Answered by
Reiny
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
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
Answered by
Mike Oxlong
dimensions
x:16 y: 16
perimeter: 64
x:16 y: 16
perimeter: 64
Answered by
Faith
256/16 =16 🙄
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