MathNet 2003 — Part 02 Question 191

As shown, $U$ and $C$ are points on the sides of triangle $M N H$ such that $M U = s$, $U N = 6$, $N C = 20$, $C H = s$, $H M = 25$. If triangle $U N C$ and quadrilateral $M U C H$ have equal areas, what is $s$?