Posted by **l** on Thursday, August 31, 2006 at 11:23pm.

Suppose the area of a rectangle is 36 square inches. Find the Minimum perimeter for a rectangle with this area.

Please help asap. Thank you! (so much)

We know that A=l*w=36 and P=2(l+w)

From the area formula we see that l=36/w

Putting this into the perimeter formula we get

P=2(36/w + w) = 72/w +2w

dP/dw= -72/w^2 +2

Set that =0 and we get -144/w^2 +2=0

2 = 72/w^2, or w^2 = 36, thus w=6 and l=6 too.

I think you should be able to prove this for the general case too.

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