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cut a paper triangle of area 1 (V Soros Olympiad 1998-99 Round 3 10.9)

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May 26, 2024
geometrygeometric inequalityareas

Problem Statement

A triangle of area 11 is cut out of paper. Prove that it can be bent along a straight segment so that the area of the resulting figure is less than s0s_0, where s0=5−12s_0=\frac{\sqrt5-1}{2}.
Note. The value s0s_0 specified in the condition can be reduced (the smallest value ofs0s_0 is unknown to the authors of the problem). If you manage to do this (and justify it), write.
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