## Triangles (a,b,c),(m,n,p) and (√(a^2+m^2),√(b^2+n^2),√(c^2+p^2))

Prove that if   $(a, \; b, \; c)$   and   $(m, \; n, \; p)$   are the lengths of the sides of two triangles then

$x \; = \; \sqrt { \,(a^2 + m^2) \,}$,        $y \; = \; \sqrt { \,(b^2 + n^2) \,}$,        $z \; = \; \sqrt { \,(c^2 + p^2) \,}$

are also the lengths of the sides of some triangle.