Posted by **Carolyn** on Monday, April 23, 2012 at 7:41pm.

Farmer Jones wants to build a recangular pen with three equalparts. He has 200 feet of fencing. What dimensions willproduce the largest pen?

- Algebra 2 -
**Damon**, Monday, April 23, 2012 at 8:04pm
Length = 3 x, width = y

4 y + 6 x = 200 so y = (200-6x)/4

or y = (100 - 3x)/2

A = area of one of the three sections = x y

A = x (100-3x)/2 = 100 x/2 - 3 x^2/2

-2 A = 3 x^2 - 100 x

-(2/3)A = x^2 - (100/3)x

x^2 - (100/3)x + 2500/9 = -(2/3)A + 2500/9

(x - 50/3)^2 = -(2/3)A + 2500/9

(x - 50/3)^2 = -(2/3)[A - 416 2/3 ]

x = 50/3

3 x = length = 50

y = (100-3x)/2 = 25

total area = 50*25 = 1250

area of each pen = 1250/3 = xy = 416 2/3

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