A rectangular pond is 7 ft longer than width. A wooden walk 1 ft long is placed around pond. Area of pond+walk=58 ft greater than area covered by pond. What are the dimensions of the pond? With Work!

Question

The pond equals seven feet plus x by x. The walk is nine feet +x by x.

Answer 1

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.