Let the width of the path be w meters. New dimensions are (20 + 2w) by (15 + 2w).
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- Solving for x, 3x = 54 - 6 = 48, so x = 48 / 3 = 16.
- The largest integer is x + 4 = 16 + 4 = 20.
- A rectangular garden measures 20 meters by 15 meters. If a path of uniform width is built around the garden, increasing the total area to 396 square meters, what is the width of the path?
- New area = (20 + 2w)(15 + 2w) = 396.
- Expanding, 300 + 70w + 4w² = 396.
- Simplifying, 4w² + 70w - 96 = 0.
