SOLUTION: A farmer has 2400 feet of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the fie

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Question 1103164: A farmer has 2400 feet of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area?

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Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
For a rectangle,
A=L%2AW
In this case, the fence perimeter only has three sides of the rectangle,
W%2BL%2BW=2400
2W%2BL=2400
L=2400-2W
Substituting into the area equation,
A=%282400-2W%29W
A=-2W%5E2%2B2400W
Get the area into vertex form by completing the square to find the max area.
A=-2%28W%5E2-1200W%2B600%5E2%29%2B2%28600%29%5E2
A=-2%28W-600%29%5E2%2B2%28360000%29
A=-2%28W-600%29%5E2%2B720000
So the max area occurs when W=600ft and is equal to 720000ft%5E2
So then from above,
A=L%2AW
L=720000%2F600
Solve for L.