MathDB
Mongolia 1999

Source:

October 30, 2008
geometry3D geometrytetrahedronLaTeXgeometry unsolved

Problem Statement

The edge lengths of a tetrahedron are a, b, c, d, e, f, the areas of its faces are S1, S2, S3, S4, and its volume is V . Prove that 2 S1 S2 S3 S4 > 3V abcdef this problem comes from: http://www.imomath.com/othercomp/jkasfvgkusa/MonMO99.pdf I was just wondering if someone could write it in LATEX form. _____________________________________ EDIT by moderator: If you type The edge lengths of a tetrahedron are a,b,c,d,e,f,a, b, c, d, e, f, the areas of its faces are S1,S2,S3,S4,S_1, S_2, S_3, S_4, and its volume is V.V. Prove that
2S1S2S3S4>3Vabcdef62 \sqrt{S_1 S_2 S_3 S_4} > 3V \sqrt[6]{abcdef} it shows up as: The edge lengths of a tetrahedron are a,b,c,d,e,f, a, b, c, d, e, f, the areas of its faces are S1,S2,S3,S4, S_1, S_2, S_3, S_4, and its volume is V. V. Prove that 2S1S2S3S4>3Vabcdef6 2 \sqrt{S_1 S_2 S_3 S_4} > 3V \sqrt[6]{abcdef}
Back to ProblemsView on AoPS