Let $ABC$ be a right triangle with $m(\widehat{A})=90^\circ$. Let $APQR$ be a square with area $9$ such that $P\in [AC]$, $Q\in [BC]$, $R\in [AB]$. Let $KLMN$ be a square with area $8$ such that $N,K\in [BC]$, $M\in [AB]$, and $L\in [AC]$. What is $|AB|+|AC|$?

$ 
\textbf{(A)}\ 8
\qquad\textbf{(B)}\ 10
\qquad\textbf{(C)}\ 12
\qquad\textbf{(D)}\ 14
\qquad\textbf{(E)}\ 16
$