A rectangular garden measures 30 meters by 20 meters. A path of uniform width is built around the garden, increasing the total area to 1,056 square meters. What is the width of the path? - Parker Core Knowledge

Understanding the Context

Why This Garden-Design Riddle Is Gaining Traction in the US

In recent years, Americans have grown more attentive to efficient land use—driven by rising urban density, rising housing costs, and evolving outdoor lifestyle preferences. The idea of adding a uniform path around a 30m x 20m plot taps into a practical, spatial challenge: how to balance open growing areas with walkways, borders, or seating zones.

This problem also reflects broader trends in smart landscaping and climate-adaptive garden design. Even a modest garden can serve as a micro-ecosystem, supporting native plants, edible crops, or native habitat restoration. A well-planned path enhances accessibility and flow while respecting available space—making it a relevant topic in modern home gardening conversations.

Key Insights

Moreover, with tools like mobile-first calculators becoming standard, users now seek fast, accurate answers that fit into busy planning routines. Converting abstract square meters into real-world dimensions like widths and areas fits perfectly with user intent—real, intentional, and mobile-optimized.

Breaking Down the Garden and Path Geometry

A rectangular garden measures 30 meters by 20 meters. A uniform path wraps completely around it, adding width x on all sides. This means new dimensions become (30 + 2x) meters in length and (20 + 2x) meters in width—the path covers the space between garden edges.

Total area after path addition is:
(30 + 2x)(20 + 2x) = 1,056 square meters

Final Thoughts

Expanding the formula:
600 + 60x + 40x + 4x² = 1,056
4x² + 100x + 600 = 1,056

Bringing all terms to one side:
4x² + 100x – 456 = 0

This quadratic equation defines the actual width of the path. Using standard solving methods