The are of the pond itself is L(L-7) where L=length. The area with the walk adds 2' to length and width making the area (L+2)(L+2-7)=(L+2)(L-5). This is 58 sq ft bigger than the area of the pond: (L+2)(L-5)-L(L-7)=58.
L^2-3L-10-L^2+7L=58; 4L=68, so L=17' and width=10'.
CHECK: Pond area=170 sq ft. Pond area+walk=19*12=228 sq ft. 228-170=58 sq ft.