A rectangular garden is 15 meters long and 8 meters wide. A path of uniform width is built around the garden, increasing the total area to 208 square meters. What is the width of the path? - Imagemakers
Why More US Garden Lovers Are Exploring Path-Surrounded Gardens
Why More US Garden Lovers Are Exploring Path-Surrounded Gardens
Ever seen a garden that feels like a crafted landscape—clean lines, deliberate space, and a smooth walking path wrapping around a central 15x8 meter plot? For many homeowners seeking both beauty and function, this setup isn’t just aesthetic—it’s a deliberate design choice growing in popularity across the US. As urban living blends with green space desires, a rectangular garden measuring 15 meters by 8 meters, framed by a uniform walking path, is sparking curiosity about optimal space use. With total area expanding to 208 square meters, users often ask: What’s the exact width of that surrounding path? Solving this combines simple geometry with real-world application—and recent searches confirm rising interest from homeowners, gardeners, and design enthusiasts alike.
How Does Expanding a Garden with a Path Work?
Understanding the Context
At first glance, the math seems straightforward: the original garden covers 15 × 8 = 120 square meters. With the path around it, the total area becomes 208 square meters. The path adds uniform width—let’s call it x—on all sides. That means the new total length is 15 + 2x and the total width is 8 + 2x. Multiplying these gives the equation:
(15 + 2x) × (8 + 2x) = 208
This quadratic equation sets the foundation for solving the path’s exact width, blending practical math with the growing trend of thoughtfully designed outdoor living.
Solving the Path Width: A Clear Step-by-Step Breakdown
To find x, expand the equation:
(15 + 2x)(8 + 2x) = 208
120 + 30x + 16x + 4x² = 208
4x² + 46x + 120 – 208 = 0
4x² + 46x – 88 = 0
Dividing by 2 simplifies it:
2x² + 23x – 44 = 0
Using the
