2025 SSMO Team Round Problems/Problem 6

Problem

The rhombus $PQRS$ has side length $3$. The point $X$ lies on segment $PR$ such that line $QX$ is perpendicular to line $PS$. Given $QX=2$, the area of $PQRS$ can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

Solution