What is the reason for the festivals of sukkot and pesach lasting seven days.
Is there a significance/reason to the number seven here?
The Rambam in Moreh Nevukhim 3:43 says that Pesach is 7 days because a seven day period is an intermediate period between the natural day and lunar month. Just as this has significance in nature (according to Munk, this refers to the medical view at the time that 7 days was a turning point in illnesses), it is significant for the Torah, because the Torah corresponds to and perfects nature. Here is the Schwartz translation:
With regard to Sukkot, the Rambam says that it is seven days so that "so that its meaning be generally known" (Pines; Schwartz: כדי שיתפרסם הדבר).