SOLUTION: Enclosing the Most Area with a Fence. A farmer with 4000 meters of fencing wants to enclose a rectangular plot that borders a river, what is the largest area tha can be enclosed?

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Question 265935: Enclosing the Most Area with a Fence. A farmer with 4000 meters of fencing wants to enclose a rectangular plot that borders a river, what is the largest area tha can be enclosed? (see figure)
river
x{ plot }x
__________
4000-2x
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
THE FORMULA IS:
X(4,000-2X)
4,000X-2X^2
2X^2-4,000X
2(X^2-2,000X)
NOW YOU NEED TO COMPLETE THE SQUARE
2(X^2-2,000X+1,000,000)=2*1,000,000
(X-1,000)^2=0
X=1,000 FOR THE SHORT SIDE MEASUREMENT.
2*1,000=2,000 FOR THE LONG SIDE.
X+X+2X=4,000
4*1,000=4,000
4X=4,000
4*1,000=4,000
4,000=4,000 FOR THE FENCE LENGTH.
AREA=2*1,000,000=2,000,000 ANS. FOR THE MAXIMUM AREA.