Answered

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

Verified Answer :

300ft x 200ft
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MissPhiladelphia

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

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