Pianos are percussion instruments according to the Hornbostel-Sachs system of categorizing musical instruments. It belongs to the percussion family because it produces sounds by striking the strings ...
You are mistaken. The piano is classified as 314.122, considered a "cordophone" because they "produce their sounds by means of the vibration of a string or strings that are stretched between fixed points." More info here.
Percussion instruments are classified idiophones.