In the diagram, ab = 12, dx = 2.5, and bx = 5. find cd. show all work.

I found your complete question in another source.
 See attached image. 
 For this case what you should see is that you have two similar triangles.
 We then have the following relationship:
 ((AB) / (BX)) = ((CD) / (DX))
 We cleared CD:
 CD = ((AB) / (BX)) * (DX)
 Substituting the values:
 CD = ((12) / (5)) * (2.5)
 CD = 6
  
 CD = 6