3. In Rt $\triangle A B C$, $F$ is the midpoint of the hypotenuse $A B$, and $D, E$ are points on sides $C A, C B$ respectively, such that $\angle D F E=$ $90^{\circ}$. If $A D=3, B E=4$, then the length of segment $D E$ is $\qquad$
3.5 .

As shown in Figure 6, extend $D F$ to point $G$ such that $D F = F G$, and connect $G B$ and $G E$.
Given $A F = F B$, we have
$\triangle A D F \cong \triangle B G F$
$\Rightarrow B G = A D = 3$
$\Rightarrow \angle A D F = \angle B G F$
$\Rightarrow A D \parallel G B$
$\Rightarrow \angle G B E + \angle A C B = 180^{\circ}$
$\Rightarrow \angle G B E = 90^{\circ}$
$\Rightarrow G E = \sqrt{G B^{2} + E B^{2}} = 5$.
Also, $D F = F G$, and $E F \perp D G$
$\Rightarrow \triangle E F D \cong \triangle E F G$
$\Rightarrow D E = G E = 5$.