This is a question that can be better answered by History scholars. I believe that Ramayana is not part of history. Rama was hero of the Epic title Ramayana' by Valmiki. This is mythological. Whatever be the position, Hindus regard rama as an avatar (incarnation) of Lord Vishnu- a Hindu god/ deity and worship him. This is a sentimental matter and many may not give a logical or authoritative answer. Personally, i shall depend on answer given by experts on History of India.
According to Hindu mythology, Ram is god who came to world and lived with people teaching them the purest way of living. That is like Jesus of western countries.
That is true Sajeetharan as lot of thing related to Christ have been found..which makes us believe that he is historic character..Regarding Rama i think it is mythological only as complete Ramayan was written..and without any historic evidence we cannot know whether it is historic figure..
Many people think that Lord Rama is a mythological figure; in leading book stores, books such as Ramayana are placed in the mythology section. As pointed out, no writer had the means to travel around the country inventing a story, fitting it into local folklore and building temples for greater credibility.