A rectangular field measures 38 meters in length and 32 meters in width. A uniform path runs along the inside perimeter of the field, covering an area of 600 square meters. What is the width of this path?

Explanation

The total area of the field is 38 × 32 = 1216 m². Let the width of the path be x meters. Then, the remaining area inside the path is (38 - 2x)(32 - 2x). The area of the path is the difference: 1216 - (38 - 2x)(32 - 2x) = 600. Expanding and simplifying leads to the quadratic equation x² - 35x + 150 = 0, which factors as (x - 30)(x - 5) = 0. Since the path width cannot be 30 meters, the width is 5 meters.