Question 6
Let $ABCD.A'B'C'D'$ be a rectangular box. Prove that a triangle can be constructed whose sides equal the distances from $A,A',D$ to the space diagonal $BD'$. Denote the box dimensions by $a_1,a_2,a_3$ and these distances by $m_1,m_2,m_3$. Determine a relation between $a_1,a_2,a_3,m_1,m_2,m_3$.