Here is more or less my method of attack:

Look in the problem statement for possible equations you could use. In this case we have a rectangle mentioned and the perimeter and area of it. So write down the equations:

and

where l is the length of the rectangle and w is the width.

You know that P = 180 m, so

We wish to maximize the area, so we need to find a value of l in terms of w (or the other way around). The obvious way to do this is:

So

Now find the w that maximizes the area.

-Dan