Why did the united staes back the south vietnamese

To prevent Communist North Vietnam from successfully conquering South Vietnam, and uniting the whole country under Communist control.

This was part of the US post war policy of Containment, designed to stop the spread of Communism to non Communist states.

The stalemate in the Korean War had shown America that their military might could not guarantee success. 142,000 US troops had been lost in the Korean War and Eisenhower knew that he could not sell to the American people the thought of sending US troops back into Southeast Asia. Hope this helps!
-K

These islands/chinampas then provided rich soil for crops with easy access to water. i hope this is correct, im so sorry if its not !