SOLUTION: A rectangular garden is to be fenced with 100 meters of fencing. The wall of the house will be one side of the garden, so the fencing is needed only on three sides. What is the lar

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Question 203860: A rectangular garden is to be fenced with 100 meters of fencing. The wall of the house will be one side of the garden, so the fencing is needed only on three sides. What is the largest garden possible?
Answer by nerdybill(7384) About Me  (Show Source):
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A rectangular garden is to be fenced with 100 meters of fencing. The wall of the house will be one side of the garden, so the fencing is needed only on three sides. What is the largest garden possible?
.
Let x = width
and y = length
.
Perimeter:
2x+y = 100
Solving for y:
y = 100-2x
.
Area = xy
Area = x(100-2x)
Area = 100x-2x^2
Area = -2x^2+100x
.
This is a parabola that opens downward -- therefore, finding the vertex gives you the maximum.
axis of symmetry = -b/(2a) = -100/(-4) = 25
.
Largest possible area then is:
Area = -2x^2+100x
Area = -2(25)^2+100(25)
Area = -1250+2500
Area = 1250 square meters