Question

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?

Answer

125 ft x 200 ft

100 ft x 105 ft

300 ft x 200 ft

105 ft x 120 ft

Answer 1

300ft x 200ft
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Answer 2

For the answer to the question above, It is 300 x 200
For the explanation, I'll write it down how I solved it.

First,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

I hope my answer helped you