4. Two sheets of the same size, each divided into seven rectangles of the same size, are placed as shown in Fig. 3, with the overlapping vertex marked as $A$, and point $C$ on the dividing line of the other sheet. If $B C=\sqrt{28}$, then the length of $A B$ is $\qquad$ .
4. $7 \sqrt{2}$.

Let $B D=x$. Then
$$
A B=A C=7 x, A D=6 x \text {. }
$$

Thus, $C D=\sqrt{A C^{2}-A D^{2}}=\sqrt{13} x$,
$$
B C=\sqrt{B D^{2}+C D^{2}}=\sqrt{14} x=\sqrt{28} \text {. }
$$

Therefore, $x=\sqrt{2}$.
So, $A B=7 \sqrt{2}$.