∵BC= 1 4 AB，∴AC= 5 4 AB，∵D为AC的中点，∴CD= 1 2 AC= 1 2 × 5 4 AB= 5 8 AB，∴BD=CD-BC= 5 8 AB- 1 4 AB= 3 8 AB=6，解得AB=16cm．答：AB的长是16cm．
