Let w=width then the length is w+15 and the area w(w+15)=9064 sq ft.
So w²+15w-9064=0. It happens that two factors of 9064 are 88 and 103, which differ by 15, so we can factorise the quadratic:
(w+103)(w-88)=0. So w=88 and w+15=103.
So the dimensions are 88' by 103'.