Lord Ram was real so was Lord krishna(whether they were really lords or just human ok that is questionable)YOu cannot fully call everything as mythology.Tell us how did we get BHARAT for our country.Do you know any other country which has given name to the land only on mythological chatrecters.note israel is the only other country named after a person called israel,though the ages that he lived ,i think it is 155yrs is wrong but you cannot say some one great israel never exixted.
Furture more the years contributed to RAm of 17000 if diffently wrong but you cannot say some on called rahuvamshi RAm never exixted. To know the actuall age of RAm you may have to scientifically find the age of the bridge and again check the the exact age provided in ramayan(the astronomical age).By the way if you something about hindu festivals we celebrate RAM navami every and even krishna ashthami(b'irtday of both of them).