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How Many Tetrahedrons?

Source: 1987 National High School Mathematics League, Exam One, Problem 8

February 24, 2020
geometry3D geometrytetrahedron

Problem Statement

We have two triangles that lengths of its sides are 3,4,53,4,5, one triangle that lengths of its sides are 4,5,414,5,\sqrt{41}, one triangle that lengths of its sides are 562,4,5\frac{5}{6}\sqrt2,4,5. The number of tetrahedrons with such four surfaces is________.
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