You can put this solution on YOUR website! Let one side =
Let the other side=
Let area =
Let perimeter=
Now substitute into area formula
This is a parabola that has a peak. I know because
of the (-) sign in front of
The peak is exactly between the x-intercepts, or at where and
because the equation is in the form
So, the max area is
This equation graphs to a convex down parabola with vertex at , telling us that the maximum area is achieved when the length of the side is . The difficulty is that the problem asks for the maximum area of a rectangle with integer side lengths. The nearest integer smaller than is 5 and the nearest integer larger than is 6.
Substituting 5 for W in gives us , so obviously substituting 6 for W in will give us . Since 5 and 6 are the nearest integers to the side length that provides the maximum area (notice that all 4 sides would be making a square) these must be the required side lengths and the maximum area for integer side lengths is
