Four. (15 points) Points
$D$ and $E$ are on
the sides $AC$
and $BC$ of
$\triangle ABC$, $\angle C$ is
a right angle, $DE \parallel AB$,
and $3 DE = 2 AB$,
$AE = 13, BD = 9$. Then, the length of $AB$ is
Four、 $\frac{15}{13} \sqrt{130}$