A rectangular enclosure with 15 rectangular partitions is to be built using 400 feet of fencing. What dimensions will produce the maximum area, and what is that area? ( length has 5 boxes and width has 3 just for extra information)

Answer 1

divide the fencing equally among lengths and widths.
There are 4 lengths and 6 widths.
So, with 200ft allocated for each, the maximum area will be when the dimensions are

200/4 by 200/6
or
50 x 33.33

or, you can do the calculus using
4x+6y = 400
A = xy
and find where dA/dx = 0