SOLUTION: you have 80 feet of fencing to enclose a rectangular region. what is the maximum area?

Question 257489: you have 80 feet of fencing to enclose a rectangular region. what is the maximum area?
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
The perimeter is
P = 2L + 2W or
80 = 2L + 2W
dividing by 2 we get
(i) 40 = L + W
THe area is
(ii) A = LW
solving (i) for L, we get
(iii) L = 40-W
substituting that in (ii), we get
(iv) A = (40-W)(W)
using completing the square, we get
A = -(W-20)^2 + 400
So, when W = 20, the max area is 400.
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