BALTIC-WAY 2004 Problem 17

Consider a rectangle with side lengths 3 and 4 , and pick an arbitrary inner point on each side. Let $x, y, z$ and $u$ denote the side lengths of the quadrilateral spanned by these points. Prove that $25 \leq x^{2}+y^{2}+z^{2}+u^{2} \leq 50$.