A rectangular garden has a length of 15 meters and a width of 10 meters. If a path of uniform width is added around the garden, increasing the total area to 300 square meters, what is the width of the path? - AIKO, infinite ways to autonomy.

Understanding the Context

Expanding this:
150 + 30w + 20w + 4w² = 300
4w² + 50w + 150 = 300
4w² + 50w – 150 = 0

Dividing the entire equation by 2 simplifies:
2w² + 25w – 75 = 0

Using the quadratic formula, w = [–25 ± √(625 + 600)] / 4
w = [–25 ± √1225] / 4
w = [–25 ± 35] / 4

Only the positive root applies:
w = (10) / 4 = 2.5

Key Insights

Thus, a uniform path width of 2.5 meters transforms the garden into a larger, harmonious space of exactly 300 square meters.

Common questions surface about how this dimension fits practical spaces—especially in compact backyard layouts. While 2.5 meters is deep, it offers comfort for walking and gathering, striking a balance between expanded area and usable square footage. Some users wonder if narrower paths limit space but forget that a 2.5-meter path strategically folds into modern design trends that value outdoor flow and versatility.

Beyond calculations, this common landscaping project reflects broader US homeowner priorities: developing outdoor areas affordably, increasing property feel, and planning for sustainable use without overspending. Additional benefits include improved drainage management, erosion control, and better access to garden features.

Myths around path width often exaggerate practical effects—some claim even 3 meters causes overuse or height issues, but research shows 2.5 meters optimizes utility within standard backyard dimensions. The increase from 150 to 300 square meters isn’t incremental in a trivial way—it represents a doubling of usable garden area with room for movement and landscaping pockets.

For homeowners considering this upgrade, this model applies to real estate trends where outdoor square footage aligns with market expectations for livable space. Whether homeowners are planning expansion, preparing for long-term living, or managing rental units, understanding path geometry informs smarter investment.

Final Thoughts

Misconceptions frequently center on impractical branding or exaggerated aesthetic impact. In reality, a 2.5-meter path blends steadily into suburban and urban landscapes, enhancing curb appeal without overwhelming smaller yards. It allows room for native planting, seating, lighting—all without reducing usable garden space.

Ultimately, this geometric approach offers homeowners a reliable method to calculate and visualize garden expansion journeys. Paired with clear math and practical values, understanding path width empowers confident decisions—whether DIY or contractor-led—toward richer, more functional outdoor spaces.

As mobility and mobile browsing grow key in consumer engagement, this topic remains relevant through active user curiosity about home design, budget planning, and sustainable improvement. By clarifying the math and broader context, readers gain not just a solution, but tools to apply elsewhere—staying informed, engaged, and empowered.

Opportunities & Considerations
Adding a uniform 2.5-meter path brings clear benefits: expanded usable area, improved drainage, and enhanced access—ideal for entertaining, gardening, or creating quiet zones. However, cost of materials, soil compaction risks, and long-term maintenance must align with budget and lifestyle. Planning ahead ensures the path integrates smoothly with future landscaping projects.