A Minesweeper Path Length

★ 8/10plane geometry Extrema Reflection analytic geometry

Problem

An engineer uses a detector, with effective range $\dfrac{\sqrt 3}2$ km, to sweep for mines in an equilateral triangular region of side length $2$ km. Starting from one vertex of the triangle, what is the minimum distance the engineer must walk to complete the sweep? Justify your answer.

Answer

Solution

Difficulty	8/10
Topics	plane geometry, Extrema, Reflection, analytic geometry

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