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 1

Let x = length and y = width

You would have 2 lengths, so 2x and 3 widths, so 3y

Those need to equal total length of fence:

2x + 3y = 1200

The 3 widths would equal total fence minus the 2 lengths:

3Y = 1200-2x

Solve for y: y = 400 -2/3x

Area = length x width = xy. Replace y :

Area = x(400-2/3x) = 400x-2/3x^2

Differentiate:

400-4x/3 =0

4x/3 = 400

4x = 1200

X = 300

Y = 400-2/3(300) = 200

The dimension would be 300 ft x 200 ft