SOLUTION: A rancher wants to enclose a rectangular field with 220 ft of fencing. One side is a river and will not require a fence. What is the maximum area that can be enclosed? Please a

Question 689772: A rancher wants to enclose a rectangular field with 220 ft of fencing. One side is a river and will not require a fence. What is the maximum area that can be enclosed?
Please and Thanks a lot!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rancher wants to enclose a rectangular field with 220 ft of fencing.
One side is a river and will not require a fence.
What is the maximum area that can be enclosed?
:
The field requires only 3 sides of fence, therefore
L + 2W = 220
L = (220-2W); we can use this for substitution in the Area equation
:
Area
A = L*W
replace L with (220-2W)
A = W(220-2W)
A = -2W^2 + 220W
A quadratic equation, max A occurs at the axis of symmetry, x = -b/(2a)
In this equation
W =
W = 55 ft is the width for max area
:
Find the max area
A = -2(55^2) + 220(55)
A = -2(3025) + 12100
A = 6050 sq/ft is the max area
:
:
Confirm this with the dimensions calculated; 110 * 55 = 6050
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