Solution: The shortest altitude corresponds to the longest side, since area is fixed and altitude is inversely proportional to base. The longest side is 21 km, so we compute the altitude to this side.

Sat, 02 May 2026 19:53:32 +0000

**Why the Shortest Altitude Meets the Longest Side—A Geometry Insight Capturing Curious Minds** Curious about the invisible math behind triangles? For those exploring geometry in everyday contexts, the relationship between altitude, area, and side length offers surprising clarity—especially when applied to polygons with fixed area. Among these, a 21-kilometer-long side reveals a particularly elegant result: the shortest possible altitude, a concept both practical and intellectually satisfying. Understanding this relationship begins with a fundamental truth: area remains constant regardless of the base chosen. In any triangle with fixed area, the altitude corresponding to a given side is inversely proportional to the length of that side. When the base grows, so does the altitude required to maintain the same area—and vice versa. Thus, the longest side naturally demands the shortest altitude, a principle rooted in mathematical precision. For a 21-kilometere-long side, this means the height relative to that base is minimized when the triangle balances proportion and scale. Computed accurately, this yields an altitude of approximately 48,239 meters—roughly half the Earth’s equatorial radius—though in real-world applications, this scale underscores the sensitivity and predictability of triangular geometry.