A rectangular garden measures 15 meters by 20 meters. 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? - Treasure Valley Movers
Discover Concerned Garden Planners, Wondering: What’s the Path Width Around a 15x20 Garden?
Discover Concerned Garden Planners, Wondering: What’s the Path Width Around a 15x20 Garden?
For homeowners seeking to enhance outdoor space with a thoughtfully designed garden, a rectangular plot measuring 15 meters by 20 meters often becomes the starting point—efficient, practical, and versatile. But when a narrow path of uniform width is added around the garden, the total area can shift dramatically, sparking curiosity about exactly how much space the path takes up. Today’s trend toward meticulous outdoor planning has boosted interest in solving this precise equation: What width does a path need to surround a 15x20 garden so the total area rises to exactly 396 square meters? This isn’t just a math problem—it’s a real-world puzzle that couples horticulture, design, and geometry.
An rectangular garden measures 15 meters by 20 meters. 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?
This scenario reflects growing interest in precision landscaping, particularly among U.S. homeowners revising how outdoor spaces integrate with sustainability, functionality, and visual harmony. The shift toward intentional garden design, driven by desire for smaller, high-impact yards, has amplified demand for clear calculations—like this one—so users can visualize space changes without guesswork.
Understanding the Context
How Does the Area Change with a Uniform Path?
Imagine a garden surrounded by a consistent border of soil or stone—this path adds width all around. Let the width of the path be x meters. The total length becomes 20 + 2x, and the width becomes 15 + 2x. Multiply these two dimensions to get the total area:
(20 + 2x)(15 + 2x) = 396
Expanding the expression:
300 + 40x + 30x + 4x² = 396
Combine like terms:
4x² + 70x + 300 = 396
Subtract 396 to form a standard quadratic:
4x² + 70x – 96 = 0
Key Insights
Divide all terms by 2 to simplify:
2x² + 35x – 48 = 0
This equation now reveals the exact width of the path, solvable via the quadratic formula: x = [–b ± √(b² – 4ac)] / (2a). Plugging in the values—a = 2, b = 35, c = –48—yields a clean, realistic result
