Farmer Ed has 450 meters of fencing, and wants to enclose a rectangular plot tha
ID: 3115851 • Letter: F
Question
Farmer Ed has 450 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence 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? 450 -2x The width, labeled x in the figure, is meters. (Type an integer or decimal.) The length, labeled 450-2x in the figure, is meters. Type an integer or decimal.) The largest area that can be enclosed is square meters. Type an integer or decimal.)Explanation / Answer
length = 450 - 2x
width = x
area = length * width
A(x) = x ( 450 - 2x )
= -2x^2 + 450x
maximum area occurs at x = -b / 2a = -450 / 2(-2)
width x = 112.5 metres
length = 450 - 2 ( 112.5)
length = 225 metres
largest area = -2(112.5)^2 + 450(112.5)
largest area = 25312.5 square metres
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