I need HELP!?

Name the original triangle ABC. Then draw hypotenuse to point D on BC. Segment AD measures 6 units, BD measures x, and CD measures 3x. Triangles ABD and CAD are similar. Corresponding parts of similar triangles are proportional. So, AD is to BD as DC is to DA. That means 6/x=3x/6. Cross multiply to get 4x^2 = 36. Now divide: x^2 = 9. We're almost done. x = 3. Go back to the original info. BC is the hypotenuse and is equal in length to 4x = 4*3 = 12. So, the last answer.