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?

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) (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 =
:
Three adjoining pens
___L__
|_|_|_|w
:
Perimeter (length of fence)
F = 2L + 4w
Replace L with
F = 2() + 4w
F = + 4w
:
Find the minimum fencing by graphing this equation: y = + 4x

You can see minimum occurs when x = 40
:
Find L: L = = 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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