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What is the minimum number of feet of fencing needed to create a rectangular garden with an area of 576ft?

Please help!!

3 answers

LOL,square

min P, given A
A = L w so L = A/w
P =2L+2w
P = 2A/w + 2 w
2 w^2 - w P = -2 A
w^2 -(P/2)w = A

w^2 -P/2 w + P^2/16 = -A + P^2/16
(w-P/4)^2 = -(1/16)(16A-P^2)
vertex when w = P/4
(that is a square :)
Area = P^2/16 = (P/4)^2 of course

P given, max A

A = L w
P =2L+2w so L = (P-2w)/2

A = (P-2w)w/2
2A = -2w^2+Pw
d(2A)/dw = -4w +P
0(max or min) when P = 4 w
that is a square :)
Hi, Im sorry Im not understanding i keep getting 144 as my answer
sqrt 576 = 24
24*4 = 96