Algebra 2
posted by Carolyn on .
Farmer Jones wants to build a recangular pen with three equalparts. He has 200 feet of fencing. What dimensions willproduce the largest pen?

Length = 3 x, width = y
4 y + 6 x = 200 so y = (2006x)/4
or y = (100  3x)/2
A = area of one of the three sections = x y
A = x (1003x)/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 = (1003x)/2 = 25
total area = 50*25 = 1250
area of each pen = 1250/3 = xy = 416 2/3