SOLUTION: A farmer has 4000 feet of fencing available to enclose a rectangular area and divide it into four plots. One side will extend beyond a barn that is 60 feet long. Fencing will not b
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Question 57121: A farmer has 4000 feet of fencing available to enclose a rectangular area and divide it into four plots. One side will extend beyond a barn that is 60 feet long. Fencing will not be needed along the barn. Let x represent the length of the side of the rectangle. Express the area A of the rectangle as a function of x. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A farmer has 4000 feet of fencing available to enclose a rectangular area and divide it into four plots. One side will extend beyond a barn that is 60 feet long. Fencing will not be needed along the barn. Let x represent the length of the side of the rectangle. Express the area A of the rectangle as a function of x.
Let x = the length of the long side
Let (x-60) = the side that uses the 60' barn.
In order to have 4 plots, 5 width sized fences required
:
Perimeter: x + (x-60) + 5w = 4000
2x - 60 + 5w = 4000
2x + 5w = 4000 + 60
2x + 5w = 4060
5w = 4060 - 2x
w = (4060/5) - (2/5)x
w = 812 - .4x
:
Area = L*W
:
Subsitute x for L and (812-.4x) for w
Area = x(812-.4x)
A = 812x - .4x^2
f(x) = -.4x^2 + 812x, the area as function of x (length)
