If the eccentricity $$e$$ of the hyperbola $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$, passing through $$(6, 4\sqrt{3})$$, satisfies $$15(e^2 + 1) = 34e$$, then the length of the latus rectum of the hyperbola $$\frac{x^2}{b^2} - \frac{y^2}{2(a^2 + 1)} = 1$$ is:

A

10

B

20

C

25

D

30