A rectangular garden measures 20 meters by 15 meters. A path of uniform width is built around it, increasing the total area to 396 square meters. What is the width of the path? - Sterling Industries
A rectangular garden measures 20 meters by 15 meters. A path of uniform width is built around it, increasing the total area to 396 square meters. What is the width of the path?
A rectangular garden measures 20 meters by 15 meters. A path of uniform width is built around it, increasing the total area to 396 square meters. What is the width of the path?
This practical landscaping question is gaining attention across the U.S. as more homeowners seek to transform outdoor spaces into functional, inviting areas—balancing beauty, usability, and value. When a rectangular garden of 20 meters by 15 meters incorporates a uniform path around the perimeter, boosting the total area to 396 square meters, solving for the path width reveals both mathematical precision and real-world design insight.
Understanding the Context
Why a rectangular garden measures 20 meters by 15 meters—and why paths around it matter now
This classic garden shape offers efficiency in layout and ease of maintenance—popular among urban and suburban gardeners alike. The evolution of outdoor living, driven by interest in sustainable spaces and improved home value, has turned small-yard optimization into a growing trend. Adding a uniform paved or mulched path not only enhances walkability and curb appeal but also helps define garden zones. With modern interest in outdoor living, understanding how added elements like paths affect space usage drives practical decision-making for homeowners.
How a uniform path around a 20×15 garden increases total area to 396 square meters
Key Insights
To find the uniform path width that transforms a 20m × 15m bed into a 396m² plot, start with basic area math. The original garden area is 20 × 15 = 300 square meters. Subtract this from the total 396m², revealing the extra space gained by the path: 396 – 300 = 96 square meters of added coverage.
Because the path surrounds the garden equally on all sides, it adds twice the path width on each dimension: one inch outward from each edge. Imagine expanding the garden by x meters on each side: the new length becomes 20 + 2x and width 15 + 2x. Area equals (20 + 2x)(15 + 2x) = 396. Multiply and simplify to reveal a quadratic equation rooted in geometry and proportion.
Common questions about A rectangular garden measures 20 meters by 15 meters. A path of uniform width is built around it, increasing the total area to 396 square meters. What is the width of the path?
When beginners explore this problem, common questions focus on unit
