How did the aztecs build their mesoamerican empire?

I was just reading about this in my World History class! 
First, we know that the Aztecs were the last of the pre-Columbian civilizations. And, we know they built several cities, their capital was Tenochtitlan. They settled on the islands of Lake Texcoco. They are most known for their chinampas, which was how they farmed! Since around them was all lakes and since they were farmers they built these things that were basically field built on top of the water! They were rooted by trees! These early Mesoamerican empires were known for their advanced technology! 

Hope this helped! 

Ps: Here's a picture from my school about this Mesoamerican empire!

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