I found width=13.72 ft and length=43.72 ft.
Call one dimension of the rectangle x, the other will be x+30
You want an area A=600 ft^2 but A=length x width=x*(x+30)=600
Rearranging you get:
[tex] x^{2} +30x-600=0[/tex]
solving this quadratic equation you get a negative solution and a positive one that gives your result.