Final answer:
The Chinese Empire reached its height at different times during the Tang, Ming, and Qing dynasties, each known for particular achievements in culture, economy, territory, and population.
Step-by-step explanation:
The Chinese Empire reached its height during different periods that are characterized by the achievements and expansion under various dynasties. The Tang Dynasty (618-907 CE) is known for its cultural achievements, economic prosperity, and substantial population growth. The Ming Dynasty (1368-1644 CE) saw significant economic success and population growth. Finally, the Qing Dynasty (1636-1911) was the last of the great imperial reigns in China, with a substantial increase in territory and population, and significant cultural developments. Therefore, Ming dynasty could be considered correct depending on the context of what 'height' refers to—be it cultural, economic, territorial expansion, population growth, or overall power.