Answer: Hence, the width of the path is 4 meters.
First we should find the area of the pool. Our width is 14 and our length is 18. In order to find the area, we must multiply these two numbers. 14 times 18 is 252. This means that the area of the pool is 252.
Since we know that one side of the pool is 18 and one side is 14, we can write out the equation below.
572= (18+2x)(14+2x)
The first thing we should do is combine like-terms.Our equation would now be as below.
x^2+16-80=0
Next we would take our quadratic equation- x=-b+-√b2-4ac/2a and fill it in with the numbers that we had in the first equation, our equation would be like below. A=1 B=16 C=-80
x=-16+-√16^2-4* 1 * -80 /2 * 1
When then simplify our equation leaving us with x=-16+-√16^2-4*1(-80)/2 * 1, which broken down is x=-16+-√+-24/2.
Lastly we must subtract and add to receive our two answers.
One side is 4 and the other is -20. Since the width of the walk cannot not be a negative number, we know that the width of the path is 4 meters.
Hence, the width of the path is 4 meters.
I hope this helped & Good Luck <3!!!