Final answer:
The first statement about Rome developing peaceful relations with Carthage as it became more democratic is false, while the second statement affirming that the Pax Romana lasted about 200 years starting with Augustus is true.
Step-by-step explanation:
The statement "As Rome became more democratic, it also developed peaceful relations with Carthage" is FALSE. During the mid-second century BCE, Rome did become a dominant power in the Mediterranean, but the expansion and wars, especially with Carthage, led to social conflicts and endangered the internal peace and unity of the Roman Republic. Political arguments were initially settled with debate and votes in the Roman tradition. However, after the sack of Carthage, this emphasis on peaceful resolution within the Roman state itself began to crumble.
The statement "The Pax Romana, which began when Augustus became emperor, lasted about 200 years" is TRUE. The Pax Romana started under Emperor Augustus's rule and was a period of peace lasting approximately 200 years. It saw minimal military expansion and was marked by political stability, despite troubles on Rome's borders and internal issues within the Empire.