13. In Rt $\triangle A B C$, $B C=3, A C=4, A B$ $=5$. If the triangle is folded so that point $A$ coincides with point $B$, then the length of the fold line is ( ).
(A) $1+\frac{\sqrt{2}}{2}$
(B) $\frac{15}{8}$
(C) $\frac{7}{4}$
(D) $\sqrt{3}$
(E) 2
13. B.

Fold the right triangle $\triangle ABC$ so that point $A$ coincides with point $B$, and the fold line is the perpendicular bisector $DE$ of side $AB$, as shown in Figure 4.
Then $\triangle ABC \backsim \triangle AED$
$\Rightarrow \frac{AD}{AC}=\frac{DE}{BC}$.
Also, $AD=\frac{1}{2} AB=\frac{5}{2}$, so
$DE=\frac{AD \cdot BC}{AC}=\frac{15}{8}$.