Question

A rectangular garden plot is to be enclosed with a fence on three of its sides and a brick wall on the fourth side. If 100 feet of fencing material is available, what dimensions will yield the maximum area? (Hint: if two of the sides are labeled w, what should the third side be called? Create a function called a(w) to analyze the area.)

Answer 1

I'll use "x" for the length, to avoid confusing the 1's and l's.
2w+x = 100
the area is thus
a = wx = w(100-2w) = 100w - 2w^2
Now just find the vertex of that parabola, and you have your width, and can then find x.

Just a note, the maximum area is achieved when the fence is divided equally among lengths and widths.