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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