3. Given that the three sides of the acute triangle $\triangle A B C$ are three consecutive positive integers, and $A B>B C>C A$. If the altitude from $A$ to side $B C$ is $A D$, then $B D-D C=(\quad)$.
(A) 3
(B) 4
(C) 5
(D) 6
3. B.

By the Pythagorean theorem, we have
$$
\begin{array}{l}
A B^{2}-B D^{2}=A C^{2}-C D^{2} . \\
\text { Then }(B D+C D)(B D-C D) \\
=(A B+A C)(A B-A C) .
\end{array}
$$

Let $A B=n+2, B C=n+1, A C=n$. Then
$$
B D+D C=n+1 \text {, }
$$

Substituting into the above equation will yield the solution.