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
Algebra.Com
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)
RELATED QUESTIONS
A farmer has 3000 feet of fencing available to enclose a rectangular field. What is the... (answered by Alan3354,stanbon)
A farmer has 5000 feet of fencing available to enclose a rectangular field. What is the... (answered by oberobic)
A gardener has 270 feet of fencing and wants to fence in a rectangular garden and then... (answered by josgarithmetic)
A farmer with 10,000 meters of fencing wants to enclose a rectangular field and then... (answered by ankor@dixie-net.com)
Max/Min Applications.
A farmer with 10,000 feet of fencing wants to enclose a... (answered by solver91311)
Hey guys im having a hard time with this word problem. Ive spent about 2 hours trying to... (answered by Theo)
A rancher with 750 ft of fencing wants to enclose a rectangular area and then divide it... (answered by stanbon,ikleyn)
This is a word problem. A farmer wishes to enclose a pasture that is bordered on one side (answered by rfer)
A farmer wishes to put a fence around a rectangular field and then divide the field into... (answered by stanbon,josmiceli)