A rectangular garden measures 15 meters by 10 meters. A path of uniform width is to be built inside the garden along its edges, reducing the gardens area by 30%. What is the width of the path? - Redraw
How to Design a Compact Garden with a Functional Path: The Math Behind a 30% Space Reduction
How to Design a Compact Garden with a Functional Path: The Math Behind a 30% Space Reduction
Curious about how small outdoor spaces can create big functionality? A growing number of U.S. homeowners are rethinking garden layouts—prioritizing both beauty and practicality. A rectangular garden measuring 15 meters by 10 meters offers a classic start, but what happens when a uniform path is woven through its edges, shrinking usable planting space while enhancing walkability and visual flow? This commonly asked question taps into a real trend: optimizing limited outdoor areas without sacrificing charm or purpose.
Recent search patterns show rising interest in efficient garden design, driven by urban living, rising land costs, and a deeper appreciation for sustainable outdoor enjoyment. Attracting attention across platforms where home improvement and lifestyle content meet, this query reflects a practical need to know how path width affects garden area.
Understanding the Context
Designing the Path: A Clear, Mathematical Response
The garden starts at 15 meters long and 10 meters wide, a total area of 150 square meters. Reducing the planting space by 30% means 70% of the garden remains usable. So the new area is:
150 m² × 0.7 = 105 m²
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Key Insights
Let the uniform width of the path be x meters. Since the path runs along all four edges, it closely follows the inner perimeter. The inner garden’s effective width and length shrink by twice the path width—2x subtracted from each dimension:
Inner width = 10 – 2x
Inner length = 15 – 2x
The new area equation becomes:
(10 – 2x)(15 – 2x) = 105
Expanding this:
150 – 20x – 30x + 4x² = 105
4x² – 50x + 150 = 105
4x² – 50x + 45 = 0
Dividing through by 1 gives:
4x² – 50x + 45 = 0
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Applying the quadratic formula:
x = [50 ± √(2500 – 720)] / 8
x = [50 ± √1780] / 8
√1780 ≈ 42.2
x = (50 ± 42.2) / 8
Two solutions emerge:
x ≈ (50 + 42.2)/8 ≈ 11.28 (too large, exceeds garden width)
x ≈ (50 – 42.2)/8 ≈ 0.975 meters
So, the practical path width is approximately 0.97 meters, a compactYet effective choice fitting most residential garden styles.
Why This Garden Layout Is Gaining Momentum
Beyond solving a space problem, this design aligns with modern priorities: clean, intentional flow; easier maintenance; improved accessibility; and a defined boundary between hardscaped and planted zones. The 30% area retention delivers balance—enough space for lush greenery, gardening, or outdoor living, minus a minimal walkway.
Studies show homeowners value gardens that serve multiple roles: recreation, relaxation, and low-effort upkeep. A narrow, uniformly planned path supports this by carving a clean, rectangular route along the garden’s heart—maximizing usable space without excess.
People越来越 appreciate this approach because it responds directly to spatial constraints in rising urban and suburban settings. It’s not about loss—it’s about smart optimization.
Common Questions About Path Width and Garden Reduction
