Ok so you want to maximize the area of the rectangle. The area of a rectangle is A=b*L (area=base*length).
We know the perimeter of a rectangle is 2(b+L)=188.
Since you want to maximize A, you want to express A with only one variable. So, you use the perimeter equation above and solve, for say L, and substitute the expression for L into your Area formula.
So now you have an equation A = ... (which only has one variable "b"). So, know you just differentiate your function and setting it equal to 0 to find the critical points.
Make sure you only consider actual physical values (if you get a negative value, for example, ignore it since you can't have a negative length).
So, then you evaluate your function A = ... at the critical points and determine which value gives the largest value for A. This will be your maximum area.