Question 6
In the diagram below, $ABCD$ is a square. Let $E$ and $G$ be two points inside square $ABCD$ and $H$ be a point on $BC$ such that $\angle AEG=\angle EGH=90^\circ$ and $EG=BH$. If $AE=13$ cm and $GH=12$ cm, what is the side length, in cm, of square $ABCD$?
