Question 2
Let $M N P Q$ be a square of side length $1$, and $A, B, C, D$ points on the sides $M N$, $N P$, $P Q$, and $Q M$ respectively such that $A C \cdot B D = \frac{5}{4}$. Can the set $\{A B, B C, C D, D A\}$ be partitioned into two subsets $S_{1}$ and $S_{2}$ of two elements each, so that each one of the sums of the elements of $S_{1}$ and $S_{2}$ are positive integers?