Final answer:
Liechtenstein is the country with the Rhine River forming its border with Switzerland and the Samina River flowing into Austria.
Step-by-step explanation:
The country that has the Rhine River forming much of its border with Switzerland, and the Samina River flowing through it into Austria, to merge with the Inn River, is Liechtenstein. This region is dominated by the Alpine ranges and is landlocked in the center of Europe, sharing borders with both Switzerland and Austria. Liechtenstein is a small principality with an area just over 160 square kilometers, making it one of the smallest countries in the world.