A rectangular garden measures 15 meters by 20 meters. If a path of uniform width is constructed around the garden, and the total area including the path is 396 square meters, what is the width of the path? - Treasure Valley Movers

Discover the Hidden Math Behind Outdoor Space Expansion

Why are homeowners and garden designers increasingly rethinking how to enhance outdoor living areas without rebuilding? A rectangular garden measuring 15 meters by 20 meters offers a compelling starting point—offering ample space that invites creative additions. Adding a uniform-width path around such a garden transforms it into a more functional and visually appealing outdoor room, especially as people seek ways to maximize small urban yards or backyard retreats. When a path of consistent width surrounds the garden, the total area grows to 396 square meters—raising a practical and intriguing question: How wide is that walkway?

This query is gaining traction across mobile devices, where users are turned on by tangible, practical problems. Combining precise geometry with real-world applications, this problem blends mathematical reasoning and everyday landscaping needs, reflecting growing interest in smart home design and outdoor productivity. The total area—396 square meters—creates a clear numerical challenge rooted in a relatable garden shape.

Understanding the expansion begins with recognizing that adding a path increases both length and width. The original garden spans 15 meters (width) by 20 meters (length). With a rectangular path uniformly placed around the perimeter, the total dimensions grow by twice the path’s width—2 w—on each side. Therefore, the new overall dimensions become (15 + 2w) meters wide and (20 + 2w) meters long.

The area formula reveals the path’s impact:
New area = (15 + 2w)(20 + 2w) = 396

Expanding this gives:
300 + 30w + 40w + 4w² = 396
4w² + 70w + 300 = 396

Subtracting 396 from both sides:
4w² + 70w – 96 = 0

This quadratic equation simplifies to a manageable form for solving with the quadratic formula:
w = [–70 ± √(70² – 4×4×(–96))]/(2×4)
w = [–70 ± √(4900 + 1536)]/8
w = [–70 ± √6436]/8

Calculating the square root and simplifying yields:
w ≈ 1.1 meters (discarding the negative root, as width must be positive)

This precise calculation proves invaluable to homeowners planning renovations—offering clarity on how much space a path will consume. The 1.1-meter width balances aesthetics and functionality, inviting gentle use of walking paths, potted gardens, or outdoor seating.

This problem isn’t just a math exercise—it reflects growing trends in American home design. With urban spaces shrinking and wellness