Let $a, b, c,$ and $d$ be the areas of the triangular faces of a tetrahedron, and let $h_a, h_b, h_c,$ and $h_d$ be the corresponding altitudes of the tetrahedron. If $V$ denotes the volume of the tetrahedron, find the maximum $k$ such that

$(a + b + c + d)(h_a + h_b + h_c + h_d) \geq kV.$

Question

Let $a, b, c,$ and $d$ be the areas of the triangular faces of a tetrahedron, and let $h_a, h_b, h_c,$ and $h_d$ be the corresponding altitudes of the tetrahedron. If $V$ denotes the volume of the tetrahedron, find the maximum $k$ such that

$(a + b + c + d)(h_a + h_b + h_c + h_d) \geq kV.$

thomas5267 · Answer

So h are the altitude of the triangles which make up the tetrahedron?

zmudz · Answer

@thomas5267 from what I understand of the problem, yes

beginnersmind · Answer

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I think it's like this.