you have a 200 feet of fencing to enclose a rectangular plot that borders a river. if you do not fence in the side along the river, find the length and width of the plot that will maximize the area. what is the largest area that can be enclosed?
Since the side along the river does not need fencing:
L + 2W = 200
Area = LW
but L = 200 - 2W, so we can substitute
Area = (200 - 2W)W
Area = 200W - 2W^2
This is a quadratic equation, so we can find the maximum area which is located at the VERTEX
Put equation into standard form
-2W^2 + 200W = 0
The W value for the vertex is given by the formula -b/2a
= -200) / 2(-2) = 200 / 4 = 50
Then L = 200 - 2(50) = 200 - 100 = 100
Therefore, the maximum area is
(100)(50) = 5000 square feet
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