A rectangular garden is 15 meters long and 10 meters wide. A path of uniform width is built around the garden, increasing the total area to 286 square meters. What is the width of the path - Treasure Valley Movers
A rectangular garden is 15 meters long and 10 meters wide. A path of uniform width surrounds it, expanding the total area to 286 square meters. What is the width of the path?
A rectangular garden is 15 meters long and 10 meters wide. A path of uniform width surrounds it, expanding the total area to 286 square meters. What is the width of the path?
In an era where small outdoor spaces are increasingly valued—especially in urban America—home gardeners are turning to clever design solutions. A rectangular garden measuring 15 meters by 10 meters, now enhanced by a narrow, uniform stone or gravel path encircling it, transforms both function and appeal. The math behind this layout reveals more than just square footage—it unlocks intelligent space planning for modern homeowners. With the total area growing to 286 square meters, the key question becomes: how wide is the path weaving around this classic garden shape? This isn’t just a gardening question—it’s a reflection of how Americans balance beauty, utility, and practicality in tighter, smarter living environments.
Understanding the Context
Why a 15m x 10m Garden with a Path Is Gaining Momentum in the US
The fusion of sustainable living, outdoor wellness, and smart space utilization is reshaping home grounds across the United States. Compact urban yards demand creative solutions, and adding a thoughtfully designed path around a rectangular garden stands out as both an aesthetic and functional choice. Social trends highlight a growing preference for usable outdoor spaces that double as relaxation zones, food gardens, or nature retreats. A uniform path around a garden blends with contemporary home design—offering definition, ease of access, and a smooth transition between zones. Plus, path usage supports low-impact landscaping, encouraging better walkability and reduced mud, which aligns with eco-conscious values. As more homeowners seek balance between beauty and practicality, this garden-adjacent feature no longer feels like luxury—it’s becoming standard practice.
How the 15m x 10m Garden and Uniform Path Calculate the Width
Key Insights
Let’s break down the math with real-world clarity. Imagine a garden plot exactly 15 meters long and 10 meters wide—area = 150 square meters. Adding a path of uniform width x all around increases the outer dimensions. The full layout becomes:
Length: 15 + 2x
Width: 10 + 2x
New area = (15 + 2x)(10 + 2x) = 286 square meters.
Expanding this:
(150 + 30x + 20x + 4x²) = 286
4x² + 50x + 150 = 286
4x² + 50x – 136 =
