SOLUTION: Here is my question. You have a rectangle with 78 square centimeters.What are the dimensions of the rectangle with the largest perimeter? Im not so sure about how to do this.

Question 569291: Here is my question.
You have a rectangle with 78 square centimeters.What are the dimensions of the rectangle with the largest perimeter?
Im not so sure about how to do this. Please help!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
You have a rectangle with 78 square centimeters.What are the dimensions of the rectangle with the largest perimeter?
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Equation:
LW = 78 sq. cm
Perimeter = 2(L + W)
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P = 2(L + (78/L))
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P = 2(L^2+78)/L
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P = (2L^2+156)/L
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Take the derivative:
P' = [L(4L)-(2L^2+156)]/L^2
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P' = [2L^2-156]/L^2
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Solve: P' = 0
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2L^2-156 = 0
L^2 = 78
Length = sqrt(78)
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Width = sqrt(78)
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Cheers,
Stan H.
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