A rectangular garden has a length of 12 meters and a width of 8 meters. A path of uniform width is built around the garden, increasing the total area to 180 square meters. What is the width of the path? - Treasure Valley Movers

Designing Outdoor Spaces with Precision: The Garden Path Puzzle

Curious about how a simple garden transforms into a refined outdoor space? The quiet fascination with rectangular garden layouts often centers on subtle design tweaks—like adding a uniform path around a 12×8 meter garden. Now, imagine adding a 180-square-meter footprint with a consistent border thickness. What’s the exact width of the path? More than a math problem, this puzzle reflects growing trends in intentional home landscaping across the US—where form meets function in small, thoughtful spaces.

Why a Rectangular Garden and Uniform Path Are Trending

Modern homeowners increasingly favor rectangular garden designs, prized for their clean lines and efficient use of space. The 12×8 meter layout is a common baseline—practical for family yards, vegetable beds, or outdoor living zones. Adding a path with uniform width elevates usability, guiding movement while enhancing curb appeal. Digital search data reveals rising interest in garden planning tools, as more Americans balance outdoor leisure with sustainable design. This combination of practicality and aesthetics isn’t just a trend—it’s a response to urban living needs and wellness-focused home environments.

How a 12×8 Meter Garden with a Uniform Path Adds Flat 180m²

Let’s clarify the core calculation. The original garden occupies 12 meters long and 8 meters wide—96 square meters. Expanding it to 180 square meters via a border means the outer rectangle grows to 180 m². With uniform width x around the entire garden, the total outer dimensions become (12 + 2x) meters by (8 + 2x) meters. Multiplying these gives:
(12 + 2x)(8 + 2x) = 180
Expanding:
96 + 40x + 4x² = 180
Simplifying:
4x² + 40x – 84 = 0
Divide by 4:
x² + 10x – 21 = 0

Solving this quadratic equation using the quadratic formula (x = [–b ± √(b² – 4ac)] / 2a), where a = 1, b = 10, c = –21, yields:
x = [–10 ± √(100 + 84)] / 2
x = [–10 ± √184] / 2
√184 ≈ 13.56
x = (–10 + 13.56) / 2 ≈ 1.78 meters

The path width is approximately 1.78 meters—adding room for easy walking without overwhelming the garden’s natural proportions.

Common Questions About the Garden Path Depth

H3: How do you calculate path width with uniform border size?
Start with the base garden