A rectangular field measures 150 meters by 200 meters. A path of uniform width surrounds the field, increasing the total area to 40,000 square meters. What is the width of the path?

Wed, 29 Apr 2026 19:22:04 +0000

**Why the Perfect Path Around a Rectangular Field Holds Attention in 2025**
A rectangular field measuring 150 meters by 200 meters sits at the center of a growing curiosity in landscaping, design, and sustainable land use. As homeowners and planners seek smarter outdoor solutions, a simple geometric puzzle has emerged: a uniform-width path circling a field boosts both functionality and aesthetics—without requiring a full redesign. Recent discussions highlight how this design balances practical space with elegant enhancement, reflecting broader trends in mindful living and property optimization. For users exploring outdoor investments, understanding the math behind such layouts reveals not just measurements—but smarter choices that align with real-world value. **The Geometry Behind a Surrounded Field: Solving the Width Mystery**
We begin with a straightforward starting point: a rectangular field of 150 meters by 200 meters, meaning the original area is 30,000 square meters. A path of equal width “w” wraps uniformly around all sides, increasing the total area to 40,000 square meters. Because the path adds space equally around the rectangle, every side of the original field gains twice the width (w) in length and width. Thus, the extended dimensions become (150 + 2w) and (200 + 2w). Multiplying these gives the total area: (150 + 2w)(200 + 2w) = 40,000. This equation forms the foundation for determining the precise width that transforms 30,000 into 40,000 square meters of usable land. **Why This Mathematical Pattern Is Gaining Traction in the US**
Across urban and suburban regions, there’s growing interest in balancing outdoor utility