I3.4 The diagonals $A C$ and $B D$ of a quadrilateral $A B C D$ are perpendicular to each other. Given that $A B=5, B C=4, C D=R$. If $D A=S$, find the value of $S$.
Suppose $A C$ and $B D$ intersect at $O$.
Let $O A=a, O B=b, O C=c, O D=d$.
$$
\begin{array}{l}
a^{2}+b^{2}=5^{2} . \\
b^{2}+c^{2}=4^{2} \ldots \\
c^{2}+d^{2}=3^{2} \ldots \\
d^{2}+a^{2}=S^{2} .
\end{array}
$$
$$
\begin{array}{l}
(1)+(3)-(2): S^{2}=d^{2}+a^{2}=5^{2}+3^{2}-4^{2}=18 \\
S=3 \sqrt{2}
\end{array}
$$