MathNet 2023 — batch of 35 questions Question 31

Let $ABC$ be a triangle with $AB = 13$, $BC = 14$, and $CA = 15$. Suppose $PQRS$ is a square such that $P$ and $R$ lie on line $BC$, $Q$ lies on line $CA$, and $S$ lies on line $AB$. Compute the side length of this square.