SEAMO 2027 - Paper F - SET 01 - Self-study Question 4

In triangle $ABC$, $\angle C=90^\circ$, $CA=3$ and $CB=4$. Point $D$ lies on $AB$ with $CD\perp AB$. Point $E$ lies on $AC$ with $DE\perp CA$. If $DE=m^2/n^2$, where $m,n$ are relatively prime, find $m+n$.

Convention: $m,n$ are positive coprime integers.