So to solve this, let's start with standard definitions. For a rectangle, A=base x height and Perimeter = 2w+2L
We know that L=2w+3 from the problem and since Area is 54 square ft, then L*w=54, therefore...
Now you have your quadratic equation!
Since you know it has rational roots, you can attempt to solve by factoring.
(w+6)(2w-9)=0. Next you separate the factors,
Since we are looking for the lengths of a rectangle, our answer cannot be negative, so we through away (w=-6) and just keep w=(9/2)
So to find length, let's plug it back into the original L equation
Hope this helps! Let me know if you have any more questions or any follow-up that I can help you with!