SOLUTION: An engineer is designing a rectangular solar panel that must have an area of 3 m2. Determine the dimensions of the solar panel with a minimum perimeter.

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Question 1050599: An engineer is designing a rectangular solar panel that must have an area of 3 m2. Determine the dimensions of the solar panel with a minimum perimeter.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%28xy=3%2C+p=2x%2B2y%29

y=3%2Fx
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p=2x%2B2%283%2Fx%29
p=2x%2B6%2Fx
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dp%2Fdx=2%2B6%28-1%29x%5E%28-2%29
dp%2Fdx=2-6%2Fx%5E2
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Any minimum of maximum for p occurs for dp%2Fdx=0.
2-6%2Fx%5E2=0
2=6%2Fx%5E2
x%5E2%2F6=1%2F2
x%5E2=6%2F2
x%5E2=3
x=0%2B-+sqrt%283%29
You must use a positive real value, so highlight%28x=sqrt%283%29%29.

y, the other dimension:
y=x%2F3
highlight%28y=sqrt%283%29%2F3%29


Just a technological graphical check if this really is a minimum:
p=2x%2B2%283%2Fx%29
p=2x%2B6%2Fx
graph%28300%2C300%2C-1%2C15%2C-1%2C15%2C2x%2B6%2Fx%29