Final answer:
The plate boundary associated with a mountain range and high plateau is a continent-continent convergent boundary, exemplified by the Himalayas and the Tibetan Plateau. This occurs through the collision of tectonic plates, resulting in mountain building and plateau elevation.
Step-by-step explanation:
The plate boundary associated with a mountain range with a high plateau on one side is typically a continent-continent convergent boundary. An illustrative example of this phenomenon is the formation of the Himalayas and the Tibetan Plateau. The collision between the Indian and Eurasian tectonic plates, which continues today, has been pushing up the Himalayan range and elevated the plateau to its remarkable height.
Mountain building, or orogeny, involves the folding, faulting, and volcanic activity that occurs when tectonic plates converge. The immense pressure and heat can lead to the creation of high elevation mountain ranges and, depending on the geologic setting, accompanying high plateaus can be formed. The Tibetan Plateau, flanked by the towering Himalayas, is an exemplary outcome of such dynamics. This plateau, also termed as 'the roof of the world', stands as the largest and highest plateau region globally owing to these tectonic processes.
Geologically, old mountain belts, such as the Urals and Appalachians, also originated from ancient convergent boundaries but have since experienced significant erosion, demonstrating the evolving nature of Earth's surface due to plate tectonics.