A tetrahedron with side lengths positive integers
Source: RMO 2008, Grade 8, Problem 1
April 30, 2008
geometry3D geometrytetrahedronpyramid
Problem Statement
A tetrahedron has the side lengths positive integers, such that the product of any two opposite sides equals 6. Prove that the tetrahedron is a regular triangular pyramid in which the lateral sides form an angle of at least 30 degrees with the base plane.