A rectangular field is 50 meters long and 30 meters wide. If a path 2 meters wide runs along the inside perimeter, what is the area of the path? - Malaeb
A rectangular field is 50 meters long and 30 meters wide. If a path 2 meters wide runs along the inside perimeter, what is the area of the path?
A rectangular field is 50 meters long and 30 meters wide. If a path 2 meters wide runs along the inside perimeter, what is the area of the path?
In an ongoing conversation about space optimization and efficient land use, a growing number of users are exploring how fixed dimensions interact with functional pathways—especially in outdoor and recreational settings. This question reflects a practical and spatial curiosity common among planners, homeowners, and designers across the United States: how much usable or transformed area is lost—or redefined—when a consistent-width path runs through the interior of a rectangular field.
A rectangular field measuring 50 meters by 30 meters becomes a focused case study when a 2-meter-wide path is built along its inner edges. This setup challenges assumptions about perimeter and usable space. Despite appearing simple, calculating the path’s area reveals subtle geometry with real-world implications for agriculture, gardening, sports fields, and park design.
Understanding the Context
Why This Problem Is Trending in the US
Auto-focused home developments, fitness circuits, and community green spaces increasingly prioritize both aesthetics and function. A wide, well-defined path inside a rectangular plot reduces usable planting or playing area, prompting thoughtful calculations to balance infrastructure with intended use. Social media discussions, DIY forums, and landscape planning blogs frequently highlight such scenarios, contributing to organic interest in precise measurements and area transformations.
Experts note this type of problem isn’t just theoretical—it anchors planning decisions affecting mobility, sustainability, and design efficiency. Understanding the true area consumed by the path enables smarter investments in land, materials, and long-term usability.
How to Calculate the Path’s Area: A Clear Breakdown
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Key Insights
A 2-meter-wide path running along the inside perimeter of a rectangular field effectively reduces usable space by narrowing the active area. The key is to compute the inner rectangle’s dimensions after accounting for the buffer zone.
The original field spans 50 meters long and 30 meters wide.
With a 2-meter path internally, each side length shrinks by twice the path width (1 meter subtracted per side):
- Adjusted length: 50 – 2×2 = 46 meters
- Adjusted width: 30 – 2×2 = 26 meters
So, the central, unoccupied area—the actual playing, growing, or exercising zone—reaches 46 × 26 = 1,196 square meters. Subtracting this from the original 50 × 30 = 1,500 square meters reveals the path covers 1,500 – 1,196 = 304 square meters.
Thus, the path spans exactly 304 square meters along the inside perimeter.
Common Questions Readers Often Ask
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