Let \( A_{1}, A_{2}, A_{3}, A_{4} \) be the areas of the triangular...

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Let \( A_{1}, A_{2}, A_{3}, A_{4} \) be the areas of the triangular faces of a tetrahedron and \( h_{1}, h_{2}, h_{3}, h_{4} \) be corresponding altitudes of the tetrahedron. If volume of tetrahedron is 5 cubic units then
\( \mathrm{P} \) find the minimum value of \( \left(\mathrm{A}_{1}+\mathrm{A}_{2}+\mathrm{A}_{3}+\mathrm{A}_{4}\right)\left(\mathrm{h}_{1}+\mathrm{h}_{2}+\mathrm{h}_{3}+\mathrm{h}_{4}\right) \) (in cubic units).

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