Question

A pool measuring 14 meters by 24 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combined is 600 square meters, what is the width of the path?

Answer 1

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 $x$.

2. The area of a rectangle is:

$A=LW$

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:

$600=(24+2x)(14+2x)$

4. Apply the Distributive property:

$600=336+48x+28x+4x^{2}\\0=-264+76x+4x^{2}$

5. When you apply the Quadratic formula, you obtain:

$x=\frac{-b\sqrt{b^{2}-4ac}}{2a}$

Where:

$a=4\\b=76\\c=-264$

Then:

$x_1=3\\x_2=-22$

Choose the positive result.

6. The answer is 3 meters.