Which river is considered China's second-longest and is crucial for the northern half of the country?

The Yellow River, also known as the Huang He, is considered China's second-longest river, following the Yangtze. It plays a vital role in the geography and history of northern China.

The Yellow River is approximately 5,464 kilometers (around 3,395 miles) long, making it a key water source for agriculture and irrigation in the northern regions of the country. Historically, it has been referred to as the "cradle of Chinese civilization" due to its significance in supporting early agricultural societies. The river's basin has been central to the development of Chinese culture and society.

Additionally, the river is essential for transportation and provides drinking water to millions of people. While the Yangtze River is longer and also significant, the Yellow River's importance to northern China, coupled with its cultural and historical significance, firmly establishes it as the correct answer in this context.

The other rivers mentioned, such as the Ganges and the Brahmaputra, are primarily associated with India and do not play a role in China's river system.