3. As shown in Figure 1, given a rectangular paper piece $A B C D, A B=3$, $A D=9$, fold it so that point $D$ coincides with point $B$, resulting in the crease $E F$. Then the length of $E F$ is ( ).
(A) $\sqrt{3}$
(B) $2 \sqrt{3}$
(C) $\sqrt{10}$
(D) $\frac{3 \sqrt{10}}{2}$
3. C.

Let $DE = x$. Then $BE = x, AE = 9 - x$.
In the right triangle $\triangle ABE$, we have
$$
3^{2} + (9 - x)^{2} = x^{2}.
$$

Solving for $x$ gives $x = 5$, so $DE = 5$.
Connecting $BD$ and intersecting $EF$ at point $G$, then $BD$ perpendicularly bisects $EF$.
In the right triangle $\triangle DEG$, we have
$$
DG = \frac{1}{2} BD = \frac{1}{2} \sqrt{3^{2} + 9^{2}} = \frac{3 \sqrt{10}}{2},
$$

thus $EG = \sqrt{DE^{2} - DG^{2}} = \frac{\sqrt{10}}{2}$.
Therefore, $EF = 2EG = \sqrt{10}$.