Answer:
The width and the length of the pool are 12 ft and 24 ft respectively.
Step-by-step explanation:
The length (L) of the rectangular swimming pool is twice its wide (W):
![L_{1} = 2W_{1}](https://tex.z-dn.net/?f=%20L_%7B1%7D%20%3D%202W_%7B1%7D%20)
Also, the area of the walkway of 2 feet wide is 448:
![W_{2} = 2 ft](https://tex.z-dn.net/?f=%20W_%7B2%7D%20%3D%202%20ft%20)
Where 1 is for the swimming pool (lower rectangle) and 2 is for the walkway more the pool (bigger rectangle).
The total area is related to the pool area and the walkway area as follows:
(1)
The area of the pool is given by:
(2)
And the area of the walkway is:
(3)
Where the length of the bigger rectangle is related to the lower rectangle as follows:
(4)
By entering equations (4), (3), and (2) into equation (1) we have:
![224 = W_{1}^{2} + 8 + 4W_{1} + 2W_{1}](https://tex.z-dn.net/?f=%20224%20%3D%20W_%7B1%7D%5E%7B2%7D%20%2B%208%20%2B%204W_%7B1%7D%20%2B%202W_%7B1%7D%20)
![224 = W_{1}^{2} + 8 + 6W_{1}](https://tex.z-dn.net/?f=%20224%20%3D%20W_%7B1%7D%5E%7B2%7D%20%2B%208%20%2B%206W_%7B1%7D%20)
By solving the above quadratic equation we have:
W₁ = 12 ft
Hence, the width of the pool is 12 feet, and the length is:
![L_{1} = 2W_{1} = 2*12 ft = 24 ft](https://tex.z-dn.net/?f=%20L_%7B1%7D%20%3D%202W_%7B1%7D%20%3D%202%2A12%20ft%20%3D%2024%20ft%20)
Therefore, the width and the length of the pool are 12 ft and 24 ft respectively.
I hope it helps you!