[thecool]

Nguyên văn bởi n.t.tuan

In this note we determine precisely when a triangle fits in a square by
finding necessary and sufficient conditions on the sides a, b, c, s for the triangle with sides a, b, c to fit into the square of side s. Our strategy is to find the side $s_{min}(T) $ of the smallest square$ S_{min} $ that contains the given triangle T; then T fits into a square S of side s precisely when $s\geq s_{min}(T) $. Scaling solves the equivalent dual problem: Find the largest triangle similar to a given triangle that fits in a given square.

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