Answer: The width of the path is 3 m.
Step-by-step explanation:
1. You know that:
- The pool measures 14 meters by 24 meters.
- The width of the path is represented by [tex]x[/tex].
2. The area of a rectangle is:
[tex]A=LW[/tex]
Where L is the lenght and W is the width.
3. If the area of the pool and the path combined is 600 m², you can write the following expression:
[tex]600=(24+2x)(14+2x)[/tex]
4. Apply the Distributive property:
[tex]600=336+48x+28x+4x^{2}\\0=-264+76x+4x^{2}[/tex]
5. When you apply the Quadratic formula, you obtain:
[tex]x=\frac{-b\sqrt{b^{2}-4ac}}{2a}[/tex]
Where:
[tex]a=4\\b=76\\c=-264[/tex]
Then:
[tex]x_1=3\\x_2=-22[/tex]
Choose the positive result.
6. The answer is 3 meters.
