Question 230068
A farmer plans to fence a rectangular grazing area along a river with 340 yards. What is the largest area he can enclose?
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Let x = width
and y = length
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Perimeter
2x + y = 340
y = 340-2x
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Area = xy
Area = x(340-2x)
Area = 340x-2x^2
Area = -2x^2 + 340x
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Axis of symmetry:
x = -b/2a = -340/(-4) = 85 yards (width)
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length:
y = 340-2x = 340-2(85) = 340-170 = 170 yards
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Area:
xy = 85(170) = 14450 square yards