Dimensions of a pool

Can someone check my work, please?

A rectangular pool is twice as long as it is wide. A small walkway surrounds the pool. The walkway is a constant 2 ft wide and has an area of 196 square feet. Find the dimensions of the pool.

What I have:

L=2w+4 and w=w+4

Area of everything= (2w+4)(w+4)
Area of the pool= (2w)w or 2w^2

To find the walkway, I subtract the area of the pool (2w^2) from (2w+4)(w+4).
2w^2+8w+4w+16-2w^2= 12w+16

12w+16= 196 -> w=15
L=2w, w=15 -> 2(15)=30

Width of the pool= 15 ft
Length of the pool= 30 ft

Juliet said:

A rectangular pool is twice as long as it is wide. A small walkway surrounds the pool. The walkway is a constant 2 ft wide and has an area of 196 square feet. Find the dimensions of the pool.

What I have:

L=2w+4 and w=w+4

Area of everything= (2w+4)(w+4)
Area of the pool= (2w)w or 2w^2

To find the walkway, I subtract the area of the pool (2w^2) from (2w+4)(w+4).
2w^2+8w+4w+16-2w^2= 12w+16

12w+16= 196 -> w=15
L=2w, w=15 -> 2(15)=30

Width of the pool= 15 ft
Length of the pool= 30 ft

Click to expand...

It looks good to me! Now check:

If the length of the pool is 30, then the length of the walkway (from one end of the pool to the other) is 34; similarly, the width (from one side of the pool to the other) is 19. Multiplying, we get a total area of 646. The pool alone is 450. Subtracting, we get 196. So your answer is confirmed.

Thank you for showing your work so nicely!