SOLUTION: A rancher needs two adjacent corrals, one for cattle and one for sheep. If a river forms one side of the corrals and 240 yd of fencing is available, what is the largest total area
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Question 354595: A rancher needs two adjacent corrals, one for cattle and one for sheep. If a river forms one side of the corrals and 240 yd of fencing is available, what is the largest total area that can be enclosed?
Perimeter = y + 3x
A = x * y
A = x(-3x+240)
A = -3x^2+240x
=-3(x^2-80x)
=-3(x^2-80x-40^2)+4800
=-3(x-40)^2+4800
Maximum total area is 4800 yards
Did I solve it correctly? Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! A rancher needs two adjacent corrals, one for cattle and one for sheep. If a river forms one side of the corrals and 240 yd of fencing is available, what is the largest total area that can be enclosed?
Perimeter = y + 3x
A = x * y
A = x(-3x+240)
A = -3x^2+240x
=-3(x^2-80x)
=-3(x^2-80x-40^2)+4800
=-3(x-40)^2+4800
Maximum total area is 4800 yards
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If both corrals have one side on the river:
2x + 2y = 240 --> y = 120-x
Area = x*2y = 240x - 2x^2
A parabola with the line of symmetry of x = -b/2a
x = -240/(-4) = 60
--> y = 60
Area = 60*120 = 7200 sq yds
