In a triangle ABC, let D be the mid-point of BC, and AM be the altitude on BC. If the lengths of AB, BC and CA are in the ratio of 2:4:3, then the ratio of the lengths of BM and AD would be

A

$$11 : 4\sqrt{10}$$

B

11 : 12

C

12 : 11

D

$$4\sqrt{10} : 11$$