4. In $\triangle A B C$, if $\angle A=2 \angle B$, side $b=4, c=5$, then side $a$ equals ( ).
(A) 6
(B) 7
(C) $3 \sqrt{5}$
(D) 5
4. A.

As shown in the figure, draw the angle bisector $AD$ of $\angle A$. By the Angle Bisector Theorem, we have
$$
\begin{array}{l}
CD=\frac{4}{9} a, BD=\frac{5}{9} a . \\
\chi \angle CDA=2 \angle DAB=
\end{array}
$$
$\angle A$,
$$
\begin{array}{l}
\therefore \triangle ADC \sim \triangle ABC . \\
\text { Hence } \frac{4 a}{9}: 4=4: a . \\
a^{2}=36, a=6 .
\end{array}
$$