SOLUTION: A rectangular yard is to be fenced in with 80 m of fence. What must the dimensions of the yard be in order to maximize the area of the field?

Question 1127353: A rectangular yard is to be fenced in with 80 m of fence. What must the dimensions of the yard be in order to maximize the area of the field?
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
Let the width be x, then the length is 80 - 2x, and the area A:
Maximize:
A(x) = x(80 - 2W)
A(x) = 80x - 2x^2
A'(x) = 80 - 4x
find A'(x) = 0
80 - 4x = 0
80 = 4x
x = 20
The maximum area is defined by a side of 20, this means that you will have a square yard.
Four sides each 20 = 20 x 4 = 80, these are your 80 m. of fence
the area is 20 x 20 = 400 m^2

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