SOLUTION: A farmer wishes to fence off three identical adjoining rectangular pens, each with 1000 feet of area,What are and so that the least amount of fence is required?

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Question 373686: A farmer wishes to fence off three identical adjoining rectangular pens, each with 1000 feet of area,What are and so that the least amount of fence is required?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A farmer wishes to fence off three identical adjoining rectangular pens,
each with 1000 sq/ft of area.
What are dimensions so that the least amount of fence is required?
:
Total area: 3(1000) = 3000 sq/ft
:
Area:
L * w = 3000
L = 3000%2Fw
:
Three adjoining pens
___L__
|_|_|_|w
:
Perimeter (length of fence)
F = 2L + 4w
Replace L with 3000%2Fw
F = 2(3000%2Fw) + 4w
F = 6000%2Fw + 4w
:
Find the minimum fencing by graphing this equation: y = 6000%2Fx + 4x
+graph%28+300%2C+200%2C+-20%2C+100%2C+-200%2C+500%2C+%286000%2Fx%29%2B4x%29+
You can see minimum occurs when x = 40
:
Find L: L = 3000%2F40 = 75 ft is the length
:
Overall dimensions of 75 ft by 40 ft for minimum fencing
:
:
Check: each pen: 25*40 = 1000 sq/ft

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