You have 1200 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in half. What are the largest dimensions of this enclosure that you could build?

Question

anonymous · Answer

|------|--------| 
|y-----|y-----|y 
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--------x----- 

Perimeter = 2x+3y where x is length and y is width 

2x+3y=1200 
3y=1200-2x 
y=400 -(2/3) x 

Area = xy = x(400-2x/3) = 400x -2x^2/3 
differentiate with respect to x 
dA/dx = 400 - 4x/3 = 0 
4x/3 = 400 
4x=1200 
x=300 feet length 
y= 400-(2/3)(300)= 200 feet 

d^2A/dx^2 = -4/3 < 0 
The area is maximized.

anonymous · Answer

125 ft x 200 ft