Question 174569
If you only have 100 feet of fencing, this means that the perimeter has a maximum of 100 feet.
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Let x = width
and y = length
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Perimeter = 2x+y
100 = 2x+y
solving for y:
y = 100 - 2x
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Area = xy
substituting in our value of y:
Area = x(100 - 2x)
Area = -2x^2 + 100x
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This is essentially a parabola that opens downward (from the coefficient -2).  So, all we need to do is to find the vertex to find the maximum.
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The x coordinate = -b/2a
The x coordinate = -(100)/2(-2)
The x coordinate = (-100)/(-4)
The x coordinate = (100)/(4)
The x coordinate = 25 feet (width)
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Length is:
y = 100 - 2x
y = 100 - 2(25)
y = 100 - 50
y = 50 feet (length)
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Area is then:
25(50) = 1250 square feet