SOLUTION: A farmer needs to build a rectangular corral for his animals. He has 200 yards of fencing available. He needs to make 4 pens. What is the largest corral he can create? (Remember th

Question 845902: A farmer needs to build a rectangular corral for his animals. He has 200 yards of fencing available. He needs to make 4 pens. What is the largest corral he can create? (Remember the pens also count as a part of the perimeter, not just the outside of the corral)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A farmer needs to build a rectangular corral for his animals.
He has 200 yards of fencing available.
He needs to make 4 pens.
What is the largest corral he can create?
:
To make 4 pens he needs 4 times the width of the corral, therefore:
2L + 4W = 200
Simplify, divide by 2
L + 2W = 100
L = (100-2W)
Total area
A = L * W
replace L with (100-2W)
A = (100-2W)*W
A = -2W^2 + 100W
A quadratic equation, max area occurs at the axis of symmetry; x = -b/(2a)
W =
W = +25 yds is the width that gives max area
Find Length
L = 100 - 2(25)
L = 50 yds length for max area
Find max area
50 * 25 = 1250 sq/yds
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