SOLUTION: A rectangular pen is made with 100m of fencing on 3 sides. The 4th side is a stone wall. Find the greatest area possible for such an enclosure.

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Question 1023610: A rectangular pen is made with 100m of fencing on 3 sides. The 4th side is a stone wall. Find the greatest area possible for such an enclosure.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Perimeter of the fence,
L%2B2W=100
Area enclosed by fence,
A=L%2AW
Substituting,
A=%28100-2W%29W
A=100W-2W%5E2
Converting to vertex form,
A=-2W%5E2%2B100W
A=-2%28W%5E2-50W%29
A=-2%28W%5E2-50W%2B625%29%2B2%28625%29
A=-2%28W-25%29%5E2%2B1250
So now in vertex form, the vertex is the maximum (since the quadratic multiplier (-2) is negative).
The maximum area occurs at W=25m and is equal to A%5Bmax%5D=1250m%5E2
L=100-2%2825%29
L=100-50
L=50 m