<PRE><B>Question 388350</B>
What is the smallest perimeter that can be used to make a rectangle with an area of 256cm squared?
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Area = LW
256 = LW
W = (256/L)
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Perimeter = 2(L+W)
P = 2(L + (256/L))
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P = 2(L^2+256)/L
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Take the derivative to get:
P&#39; = 2[(L^2+256)-L(2L)]/L^2
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Solve: 2[(L^2+256)-L(2L)]/L^2 = 0
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Solve: L^2+256-2L^2 = 0
-L^2 = -256
L^2 = 256
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L = sqrt(256) = 16
Therefore W = sqrt(256) = 16
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Perimeter = 4*16 = 64
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Cheers,
Stan H.
</PRE>