A man built a walk of uniform width around a rectangular pool. If the area of the walk is 253 square feet and the dimensions of the pool are 6 feet by 6 feet, h

Question

A man built a walk of uniform width around a rectangular pool. If the area of the walk is 253 square feet and the dimensions of the pool are 6 feet by 6 feet, how wide is the walk?

Answer 1

Let x = width of walkway

 

The pool and the walkway combined form a square with sides of length 2x+6.

 

(2x+6)(2x+6) - (6)(6) = 253

 

4x² + 24x + 36 - 36 = 253

 

4x² + 24x - 253 = 0

 

x = [-24 ±√4624]/8 = [-24±68]/8 = 5.5 or -11.5

 

Since x can't be negative, x = 5.5 feet