设CD=Y,则BD=4Y.
∠ADB=∠BAC=90°;∠B=∠B.则:⊿BAD∽⊿BCA.
得AB/BD=BC/AB,AB^2=BD*BC=4Y*5Y=20Y^2,AB=2√5Y.
所以,AB:BC=2√5Y:5Y=2√5:5.