Answer:
3 feet
Step-by-step explanation:
The diagram showing the pool and the walkway has been attached to this response.
The area of the pool = 15feet x 17 feet = 255 square feet
The total area of the pool and the walkway = 483 square feet
The area of the walkway is the difference between the total area and the area of the pool. i.e
Area of walkway = total area - area of pool
Area of walkway = 483 - 255 = 228 square feet
Now, from the diagram, the walkway can be seen as four rectangles - A, B, C and D - all with a width of x.
Area of rectangle A = (17 + 2x) * x = 17x + 2x²
Area of rectangle B = (17 + 2x) * x = 17x + 2x²
Area of rectangle C = 15 * x = 15x
Area of rectangle D = 15 * x = 15x
Area of walkway = Area of rectangle A + Area of rectangle B + Area of rectangle C + Area of rectangle D
228 = [17x + 2x²] + [17x + 2x²] + [15x] + [15x]
228 = 64x + 4x²
4x² + 64x - 228 = 0
Divide through by 4
x² + 16x - 57 = 0
Now let's solve the quadratic equation:
x² - 3x + 19x - 57 = 0
x(x - 3) + 19(x - 3) = 0
x - 3 = 0 or x + 19 = 0
x = 3 or x = -19
Since width cannot be negative, the correct solution is x = 3
Therefore, the width of the walkway is 3 feet
