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Miklós Schweitzer 1953- Problem 7

Source: Miklós Schweitzer 1953- Problem 7

August 2, 2015

3D geometrycollege contests

Problem Statement

7. Consider four real numbers

t_{1},t_{2},t_{3},t_{4}

such that each is less than the sum of the others. Show that there exists a tetrahedron whose faces have areas

t_{1},t_{2}, t_{3}

and

t_{4},

respectively. (G. 9)