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