This is the 5959th most frequent Japanese word.
れき
"れき" (reki) can mean "history" or "record" depending on context.
In this sentence, 'れきとした' is derived from '歴史' meaning history, referring to the distinguished nature of the family.
彼は長いれきとした歴史のある家系に属している。
He belongs to a family with a distinguished and long history.
Here, 'れき史的' connects to '歴史', describing the historical significance of the buildings.
この町には古いれき史的な建物がたくさんあります。
There are many historic buildings in this town.
In this context, 'れき然たる' signifies 'distinguished', showcasing the exceptional quality of her decision-making.