A rectangular garden measures 15 meters by 10 meters. A path of uniform width runs inside the gardens perimeter, reducing the planting area to 96 square meters. What is the width of the path? - Malaeb

Understanding the Context

Why This Garden Layout Is Trending in US Homes

The rectangular 15x10 meter garden isn’t just a default choice—modern homeowners value clean symmetry and efficient space planning. Adding a consistent-width path inside tightens outdoor aesthetics while creating a defined walkway. Designers and gardeners nationwide are reimagining such layouts to accommodate outdoor living with both style and sustainability.

This trend reflects shifting priorities: thoughtful yard design that serves daily routines without losing charm. Social platforms and gardening forums now highlight projects emphasizing precise measurements, with shared equations like the path-width problem offering clarity. Users seek reliable ways to estimate layouts—especially when optimizing paths, plant beds, or irrigation without guesswork.

Key Insights

How to Calculate the Path Width Using Simplified Math

While the scenario appears straightforward, analyzing the planting area requires a precise spatial breakdown. Imagine a rectangle 15m long and 10m wide, with a path uniformly narrowing each side by x meters. The inner planting zone then becomes (15 – 2x) meters long and (10 – 2x) meters wide. The area of this zone equals 96 square meters.

We formulate the equation:
(15 – 2x)(10 – 2x) = 96

Expanding:
150 – 30x – 20x + 4x² = 96
4x² – 50x + 150 – 96 = 0
4x² – 50x + 54 = 0

Final Thoughts

Dividing through by 2 gives:
2x² – 25x + 27 = 0

This quadratic equation reveals the path width x—a realistic positive solution that keeps both plant space and walkway functional. Solving using the quadratic formula confirms the width fits design logic, enhancing outdoor usability without overcrowding.

Common Queries About the 15x10 Meter Garden with Path

H3: What exact width removes 54 square meters of planting area?
The path measures 1.2 meters wide, shrinking the planting zone from 150 to 96 square meters. This balance supports both easy access and vibrant plant beds.

H3: Does the path go Along the Entire Perimeter?
Yes—its uniform width runs the full inner edge, symmetrically reducing width and length on all sides, a key factor in maintaining layout harmony.