KöMaL 2023 B5327

The heights of triangle $ABC$ are $m_a$, $m_b$ and $m_c$. Suppose that one can construct a triangle having sides $m_a$, $m_b$ and $m_c$, and the heights of that triangle are $x$, $y$ and $z$. Show that one can again construct a triangle having sides $x$, $y$ and $z$.