Answer:
Let x be the width of the pool. Then the length of the pool is 2x, since it is twice as long as it is wide.
The area of the pool is (2x)(x)=2x^2
The total area of the pool and the walkway is 2x^2+196 square feet.
We can set up the equation using this information:
2x^2 + 22x = 196
Where 22x is the area of the walkway, 22x = 2x * 2 = 4x
2x^2 + 4x = 196
2x^2 + 4x - 196 = 0
Using the quadratic formula to solve the equation above:
x = (-b ± √(b^2 - 4ac))/2a
x = (-4 ± √(4^2 - 42196))/2*2
x = (-4 ± √(16 - 1568))/4
x = (-4 ± √(-1552))/4
Since x is width of the pool, it cannot be a negative value, the x value that is negative must be rejected. Therefore x = (-4 + √1552)/4 = 8
The width of the pool is 8 feet and the length is 2x = 2*8 = 16 feet