Let CEP = α,

Because tan∠BPD= 1/2, tan∠CEP=tanα=2.

tan∠A = tan( 180-2α)=-tan 2α=-2 tanα/( 1-tanα)= BC/AC

Substitute AC=3 and tanα=2 to get BC. Then AB is obtained according to Pythagorean theorem. Finally, AC+AB+BC is enough.