A rectangular garden has a length of 42 meters and a width of 28 meters. A path of uniform width is built around the garden, increasing the total area to 1,800 square meters. What is the width of the path? - RTA
A rectangular garden has a length of 42 meters and a width of 28 meters. A path of uniform width is built around the garden, increasing the total area to 1,800 square meters. What is the width of the path?
A rectangular garden has a length of 42 meters and a width of 28 meters. A path of uniform width is built around the garden, increasing the total area to 1,800 square meters. What is the width of the path?
Imagine a well-designed outdoor space transforming your backyard into a peaceful retreat—this exact scenario plays out when homeowners add a walkway around a rectangular garden. Characterized by precise geometry and thoughtful landscaping, this setup is gaining attention in U.S. home design circles, where functional beauty meets spatial efficiency.
A rectangular garden measuring 42 meters long and 28 meters wide offers a solid footprint, but adding a uniform path around it significantly expands usable space without altering the garden’s original proportions. When, with a path of equal width surrounding the entire area, the total landscape grows to 1,800 square meters, the question becomes clear: How wide must the path be?
Understanding the Context
Why This Garden Design Is Trending in the U.S.
Recent survey data shows increasing interest in creating multi-functional outdoor environments—spaces that support relaxation, gardening, and small social gatherings. A uniform path enhances accessibility and aesthetic balance, particularly in suburban homes where outdoor living areas are central to daily life. As home trends shift toward maximizing usable space within defined boundaries, precise calculations to integrate features like paths have become common among DIY enthusiasts and professionals alike.
This combination of structured planning and outdoor integration taps into a broader movement: blending landscape architecture with practical living—efficient, intentional, and enjoyable.
How to Calculate the Path Width—A Clear Explanation
Key Insights
To determine the uniform width of the path surrounding the garden, we begin by defining variables:
- Garden length: 42 meters
- Garden width: 28 meters
- Path width: unknown, let this be x meters
- Total outer dimensions: (42 + 2x) by (28 + 2x)
- Total area with path: (42 + 2x)(28 + 2x) = 1,800 square meters
Expanding this expression:
(42 + 2x)(28 + 2x) = 42×28 + 42×2x + 28×2x + 4x²
= 1,176 + 84x + 56x + 4x²
= 1,176 + 140x + 4x²
Set this equal to 1,800:
1,176 + 140x + 4x² = 1,800
Rearranging:
4x² + 140x + 1,176 – 1,800 = 0
4x² + 140x – 624 = 0
Divide entire equation by 4 to simplify:
x² + 35x – 156 = 0
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Solving for the Path Width
Using the quadratic formula:
x = [–35 ± √(35² + 4×156)] / 2
x = [–35 ± √(1,225 + 624)] / 2
x = [–35 ± √1,849] / 2
√1,849 ≈ 42.99
x = [–35 + 42.99] / 2 ≈ 7.99 / 2 ≈ 3.995
(We reject the negative root as path width must be positive.)
Rounded, the path width is approximately 4 meters—a measurable adjustment that transforms how outdoor space functions.
Common Questions About Path Dimensions and Garden Expansion
1. Why does the total area increase so much?
The expansion results from extending both length and width by 2x—the path adds 2x to each dimension, leading to nonlinear growth. This demonstrates why precise area calculations are essential when redesigning outdoor layouts.
2. Is 4 meters a realistic path width?
Yes. At four meters, the path remains proportionate to the original garden (42m × 28m), enhancing usability without overwhelming the space. It balances aesthetics with functionality commonly preferred in U.S. backyard designs.
3. Does a 4-meter path impact plant beds or garden access?
No—once calculated, the path surrounds evenly, maintaining walkable margins and allowing flexibility for planting zones either inside or adjacent to the walkway, supporting both design and usability goals.
Opportunities and Practical Considerations
A uniform path improves accessibility—ideal for accessibility needs or large family gatherings. Yet, installation requires attention to topography, drainage, and long-term maintenance. Budgeting for materials and leveling ensures durability, especially in regions with varied weather.
