Question
how long do bananna trees live?

Answer
Mario,

It really depends on where you live.  They are a perennial species which means they will live for several seasons at least.  

There are a couple of species that will survive in USDA Zone 4.  We grow bananas at our crops of the world garden at Illinois State, however we bring these inside for the winter.  

If you asking about the type that produces bananas like we buy at the store, these are strictly tropical.  

I hope this helps.

Good luck in the garden.

Gary