A rectangular field measures 120 meters by 80 meters. If a path of uniform width is constructed around the field, and the total area of the field and path together is 13,600 square meters, what is the width of the path? - Treasure Valley Movers
The quiet math behind a field and a path: how precise planning shapes outdoor spaces
The quiet math behind a field and a path: how precise planning shapes outdoor spaces
Curious about how a simple rectangular plot evolves with a surrounding walkway? You’re not alone. In suburban planning, small landscaping miscalculations can significantly impact space and comfort—especially when a consistent border reshapes usable area. The question: A rectangular field measures 120 meters by 80 meters. If a path of uniform width wraps around the field, and the total area—field plus path—is 13,600 square meters, what is the width of that path? is gaining quiet attention across the U.S. Because smart land use matters more than ever, from garden design to smart home planning, and precise measurements drive real-world decisions.
Why This Question Is Trending Now
Understanding the Context
Across cities and neighborhoods, outdoor living spaces are being reimagined. Rising interest in organic home grounds, accessible landscapes, and smart yard design fuels demand for accurate planning tools. This problem reflects current trends where people weigh subtle design choices—like path width—not just for aesthetics, but for functionality, drainage, and property value. People search for precise answers not just to build walkways, but to maximize space, reduce erosion, and maintain clear sightlines. The specificity of a 120m by 80m field with a total area of 13,600 square meters makes it a tangible, relatable case that stands out in search algorithms.
Understanding the Problem: Field + Path = Expanded Area
Imagine a flat rectangle measuring 120 meters long and 80 meters wide—its area is exactly 9,600 square meters. Now add a border of uniform width around the perimeter. This increases both length and width by twice the path width (once on each side). So if the path is x meters wide, the outer dimensions become (120 + 2x) by (80 + 2x). The total area then equals 13,600 square meters. From basic algebra, you solve for x by expanding:
$$
(120 + 2x)(80 + 2x) = 13,600
$$
Expanding gives:
$$
9600 + 400x + 4x^2 = 13,600
$$
