A rectangular swimming pool is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a 2 feet wide and has an area of 448 square feet including the pool. Find the dimensions of the pool

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):

Also, the area of the walkway of 2 feet wide is 448:

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:

By solving the above quadratic equation we have:

W₁ = 12 ft

Hence, the width of the pool is 12 feet, and the length is:

Therefore, the width and the length of the pool are 12 ft and 24 ft respectively.

I hope it helps you!                                                                                          

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