Hmm...now that is a good question. I am sorry, I do not have an answer, only the maths behind it.

If we do some simple algebra, 2L + 2W = 16 simplify this and we get W = 8-L

The A(rea) = LW

So A = L(8-L)

A = 8L - L^{2}

You will get an upside down parabola with the maximum at (4,16) so the maximum area is when the length is four feet, 16 feet squared. If you go either side of this number, ie, go above or below four, the area decreases.