Final answer:
The Incas built the Royal Road of the Mountains, an extensive road system that was critical to the efficiency and success of their empire.
Step-by-step explanation:
The Incas were indeed remarkable engineers and constructed an extensive and sophisticated network of roads throughout their empire. The correct answer to the student's question about the engineering marvel that was 30 feet wide and walled for its entire 3,750 miles is E. Royal Road of the Mountains.
This road system allowed for efficient communication and movement of armies, goods, and people across the diverse and challenging Andean landscape. The Incas built monumental buildings, extensive road systems, and harnessed the land with terraced hillsides, as seen in the iconic settlement of Machu Picchu high in the mountains.