The perimeter of a rectangle window is 32 ft Find the dimens

The perimeter of a rectangle window is 32 ft. Find the dimensions of the window that will enclose the largest area.

Solution

Let W = width
and L = length
.
Since perimeter is:
2(L + W) = 32
L + W = 16
L = 16-W
.
Area = W(16-W)
Area = -W^2 + 16W
.
By inspection, we see (from the -1 coefficient associated with W^2) that it is a parabola which opens downward -- therefore, the \"axis of symmetry\" should give you the max.
.
Axis of symmetry:
W = -b/2a
W = -16/2(-1)
W = 8 feet (width)
.
Length:
16-W = 16-8 = 8 feet (length)