The story
- Proto-Indo-European*strengʰ-
- Proto-Germanic*strangaz
- Proto-West Germanic*strang
- Proto-West Germanic*strangiþu
- Old Englishstrengþu
- Middle Englishstrengthe
- Middle Englishstrengthen
- Middle Englishstrengthenen
- English todaystrengthen
From rare Middle English strengthenen (14th c.), from earlier strengthen (12th c.), where -en is the infinitive ending. Probably the original form was reinterpreted as strength + -en around the time when the infinitive ending was being apocopated in late Middle English.
Etymology from Wiktionary, CC BY-SA 4.0.