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Oliga [24]
3 years ago
11

Miguel buys 100 feet of fence to enclose a rectangular area of his backyard so his dog can run freely. What is the maximum area,

in square feet, he can enclose?
Mathematics
1 answer:
sdas [7]3 years ago
5 0
Suppose the length of the triangle is x, if the perimeter of the rectangle is 100 ft, the width of the rectangle will be (50-x) ft.
Area of rectangle will be:
A=length*width
A=x(50-x)
A=50x-x^2
at maximum area, dA/dx=0
thus
dA/dx=50-2x=0
solving for x we get
2x=50
x=25
thus for maximum area length=25 ft
the size of the width will be
50-x=50-25=25 ft
thus the maximum area will be:
25*25=625 sq. feet
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