Algebraic Area Problem?

A rectangular fish pond is 7 ft longer than it is wide.

A wooden walkway 1 ft wide is placed around the pond.

The area covered by the pond and walkway is 58 square feet

greater than the area covered by the pond alone.

What are the dimensions of the pond?

(W + 2)(W + 9) - W(W + 7) = 58

2W - 40 = 0

W = 20

The fish pond is 27 ft long and 20 ft wide.

Hello hlh6591, let the length be 7+w of the pond. Its area will be 7w + w^2

As walk way is included, then length would be 9+w and width w+2

So area of pond and walkway together w^2 + 11w + 18

Given w^2 +11w+18 - w^2 -7w = 58

===> 4w = 40

So w = 10 ft

Length = 17 ft

Verification: Pond 17 x 10 and with walkway 19 x 12

Area difference 228 - 170 = 58 sq ft. YES VERIFIED