"Adult" depends on territorial influences, culture and laws. In the US, in most states, 16 is considered adult for a few things (like quitting school or working outside the home), 18 is considered an adult for some purposes (driver's license, cigarettes, voting), 21 for others (alcohol and everything else), 25 for earned income credit, and 27 for lower auto insurance costs. One can also be emancipated, and therefor an adult by legal standing.
If the person in question is Hispanic, Catholic, or Jewish (just as examples), adulthood comes at 13, when one can legally marry. That is an aspect of culture and religion. A 13 year old can also be tried as an adult for capital crimes.
Citing Juliet would be a cultural definition of adulthood, as it was common during her timeframe. Mohammed's instance would be one of culture and religion (he was raised in an atmosphere of Christianity, Judaism, and tribal beliefs), which gave not only freedom of age selection, but also quantity of spouses. Poe's selection of spouse did not go without mention, and it cost him dearly during America's Victorian prudishness in culture and laws, not just for her age but also her relation to him.