Final answer:
Italy was the Allied Power that grew in size from territories taken from Austria-Hungary and Russia after joining the Allied Powers in World War I, motivated by territorial gains promised by the Treaty of London and to reclaim lands with Italian populations from Austro-Hungarian control.
Step-by-step explanation:
The Allied Power that grew larger thanks to land taken from Austria-Hungary and Russia was Italy. Originally part of the Triple Alliance with Germany and Austria-Hungary, Italy had declared neutrality at the onset of World War I. However, Italy later joined the Allied Powers in early 1915, inspired by the potential for territorial gains. The Treaty of London in 1915 promised Italy the territories of South Tyrol, Trentino, and parts of Dalmatia along the Adriatic coast, which were under Austro-Hungarian rule. Similarly, Italy was eyeing territories inhabited by Italian populations but controlled by Austria-Hungary. After Italy's switch of sides and participation in the war on the side of the Allies, it gained these territories as a reward for its contributions to the war effort, which expanded its size and influence post-war.