A 23-ft by 47-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 456ft^2, how wide is the walkway?

Answer:The wide of the walkway is 3 feetStep-by-step explanation:* Lets explain how to solve the problem- A 23-ft by 47-ft rectangular swimming pool is surrounded by a  walkway of uniform width- Assume that the uniform width is x- That means each dimensions of the the rectangular pool will exceed  by 2x (x from each side)- The dimensions of the pool with the walkway are 23 + 2x and 47 + 2x- The total area of the walkway is the difference between the area of  the pool with walkway and the area of the pool- Area of any rectangle = l × w, where l, w are its dimensions∴ The area of the pool = 23 × 47 = 1081 ft²∴ The area of the pool with walkway = (23 + 2x)(47 + 2x)∴ The area of walkway = (23 + 2x)(47 + 2x) - 1081 ⇒ (1)∵ The area of the walkway is 456 ft² ⇒ (2)- Equate (1) and (2)∴ (23 + 2x)(47 + 2x) - 1081 = 456- Add 1081 for both sides∴ (23 + 2x)(47 + 2x) = 1537- Multiply 2 brackets∴ (23 × 47) + (23 × 2x) + (2x × 47) + (2x × 2x) = 1537∴ 1081 + 46x + 94x + 4x² = 1537∴ 1081 + 140x + 4x² = 1537- Subtract 1081 from both sides∴ 4x² + 140x - 456 = 0- Divide all terms by 4 because 4 is a common factor in all terms∴ x² + 35x - 114 = 0- Factorize it∴ (x - 3)(x + 38) = 0- Equate each bracket by 0∴ x - 3 = 0- Add 3 for both sides∴ x = 3 OR∴ x + 38 = 0- Subtract 38 from both sides∴ x = -38 ⇒ rejected because no negative answer for dimensions∴ The value of x is 3* The wide of the walkway is 3 feet