Final answer:
Costa Rica is the country that has both the San Juan River, flowing out of Lake Nicaragua, and the Terraba River.
Step-by-step explanation:
The country that has the San Juan River, which flows out of Lake Nicaragua, as well as the Terraba River, is Costa Rica. The San Juan River serves as a part of the border between Nicaragua and Costa Rica, while the Terraba River is located entirely within Costa Rica. Lake Nicaragua, the largest lake in Central America, is situated within the borders of Nicaragua. Both Nicaragua and Costa Rica are known for their biodiversity and are significant tourist destinations in Central America.