3. As shown in Figure 1, in the right triangle $\triangle ABC$, $AB = BC = 8$, points $E$ and $F$ are on sides $AB$ and $BC$ respectively, with $AE = 3$, $CF = 1$, and $P$ is a moving point on the hypotenuse $AC$. Then the minimum value of the perimeter of $\triangle PEF$ is ( ).
(A) $4+\sqrt{74}$
(B) $4 \sqrt{2}+\sqrt{74}$
(C) $4 \sqrt{5}+\sqrt{74}$
(D) $8+4 \sqrt{2}$
3. C.

As shown in Figure 7, construct the symmetric point $E^{\prime}$ of point $E$ with respect to $A C$, and connect $E^{\prime} F$. Then the minimum value of $P E + P F$ is exactly the length of segment $E^{\prime} F$.
Construct $E^{\prime} G \perp B C$ at point
G. Then
$$
E^{\prime} G = A B = 8, F G = 4 .
$$

By the Pythagorean theorem, we get
$$
\begin{array}{l}
E^{\prime} F = \sqrt{8^{2} + 4^{2}} = 4 \sqrt{5}, \\
E F = \sqrt{5^{2} + 7^{2}} = \sqrt{74} .
\end{array}
$$

Therefore, the minimum perimeter of $\triangle P E F$ is $4 \sqrt{5} + \sqrt{74}$.