A rectangular garden has a length of 15 meters and a width of 10 meters. A path of uniform width surrounds the garden, increasing the total area to 264 square meters. What is the width of the path? - Treasure Valley Movers
Why Household Landscapes Are Evolving – The Hidden Math of Garden Pathways
Why Household Landscapes Are Evolving – The Hidden Math of Garden Pathways
Tired of standard backyard designs? Many U.S. homeowners are reimagining outdoor spaces with smarter, more functional features—like rectangular gardens framed by carefully planned pathways. This trend isn’t just aesthetic: strategic garden planning offers both beauty and practicality. A notable example is a 15-meter-by-10-meter rectangular garden, bordered by unfolding pathways that transform simple yard space into a purposeful extension of interior living. But here’s the intriguing question: when such a garden gains a uniform path width, how does the total area expand—specifically to 264 square meters—and what’s the most accurate width for that path? Exploration reveals a precise calculation grounded in geometry and real-world design, offering clarity for those planning thoughtful outdoor renovations.
Understanding the Context
Why a Rectangular Garden with a Path Is Gaining Popularity in the U.S.
As urban living shrinks available space and sustainability rises, functional yet elegant outdoor environments are in demand. Rectangular gardens paired with uniform pathways reflect this dual focus—optimizing both usable area and curb appeal. Recent data shows a growing interest in modular garden solutions, where every square meter counts. A uniform path around the bed offers seamless flow, improved accessibility, and enhanced landscaping hierarchy. With the specific setup of a 15m × 10m garden expanding to 264m² total, the question isn’t just technical—it’s about maximizing value without sacrificing style or practicality.
How Does It Work? Calculating the Path Width Behind the Math
Key Insights
Given a rectangular garden of 15 meters (length) by 10 meters (width), the full total area including a uniform path of width x meters becomes:
(15 + 2x) × (10 + 2x) = 264 square meters
Expanding this:
150 + 30x + 20x + 4x² = 264
Simplify to:
4x² + 50x + 150 = 264
4x² + 50x – 114 = 0
Divide through by 2:
2x
