---Question: A cartographer is creating a rectangular map with a fixed perimeter of 100 km. What is the largest possible area (in square kilometers) of the map that can be represented under this constraint?

Mon, 04 May 2026 18:54:54 +0000

--- **Intro: The Geography of Efficiency—Why a Simple Rectangle Matters**
When new maps are born from exact measurements, a timeless question stirs among designers and geospatial professionals: what rectangular shape maximizes area under a fixed perimeter? This isn’t just a math puzzle—it’s woven into urban planning, real estate design, logistics, and digital mapping interfaces. As precision in spatial planning rises, the pursuit of optimal land use in fixed boundaries reveals surprising insights. A 100-kilometer perimeter is a familiar challenge, sparking curiosity about efficiency in a world where space shapes clusters, routes, and growth. In the US, from suburban expansion to infrastructure projects, understanding this geometric principle supports smarter decision-making. This guide uncovers the optimal rectangular layout that delivers the largest area—and why it matters. --- **Why This Question Is Rising in US Discussions**
The demand to maximize space within limits aligns with growing urban density and sustainable design trends in the US. Cities increasingly face pressure to develop efficiently without waste. Digital mapping tools, from real estate platforms to navigation apps, rely on geometric precision to guide users and planners alike. As location-based services expand and modular spatial planning becomes more common, the math behind a perfect rectangular configuration gains relevance. The “how” touches on efficiency, cost savings, and spatial optimization—key themes in both civic and commercial contexts.