This is the 11276th most frequent Korean word.
길어져
"길어져" means "to become longer" in English.
In this sentence, "길어져서" refers to the act of duration becoming longer in terms of time.
회의 시간이 계속 길어져서 지쳤다.
The meeting time kept extending, so I got tired.
Here, "길어졌다" indicates that the physical length of the road increased.
이 도로는 최근 공사로 더 길어졌다.
This road became extended recently due to construction.
In this case, "길어져서" describes the increase in the length of hair over time.