You have a 1200-foot roll of fencing and a large field. you want to make two paddocks by splitting a rectangular enclosure in half. what are the dimensions of the largest such enclosure?

Let width = w

Let length = l

Let area = A

3w+2l=1200

2l=1200-3w

l=1200-3/2

A=w*l

A=w * (1200-3w) / 2

A=600w - (3/2) * w^2

If I set A=0 to find the roots, the maximum will be at wmax=-b/2a which is exactly 1/2 way between the roots - (3/2) * w^2+600w=0

-b=-600

2a=-3

-b/2a=-600/-3

-600/-3=200

w=200

And, since 3w+2l=1200

3*200+2l=1200

2l = 600

l = 300

The dimensions of the largest enclosure willbe when width = 200 ft and length = 300 ft

check answer:

3w+2l=1200

3*200+2*300=1200

600+600=1200

1200=1200

and A=w*l

A=200*300

A=60000 ft2

To see if this is max area change w and l slightly but still make 3w+2l=1200 true, like

w=200.1

l=299.85

A=299.85*200.1

A=59999.985