The three statements that are true about the Punic Wars are:
1. The Punic Wars were fought between Rome and Carthage.
2. After the Punic Wars, Rome controlled the region of the Mediterranean.
3. Carthage became a Roman province.
The statement "Carthage won the Punic Wars" is false. The statement "Rome fought a tribe located on the Italian peninsula" is not related to the Punic Wars, so it is also false. The statement "The Punic Wars didn't last long" is subjective, but generally not considered true as the wars lasted for over a century, with intermittent periods of conflict.