Thinking about Sarah's situation - about giving up hope that she and her husband, Abraham, would ever be parents.

When Sarah decided to give her handmaid, Hagar, to Abraham, Sarah's bio-clock was ticking like big ben - if she wasn't already going through the change-of-life...  She was in her mid 70s - they lived longer back then.  i believe, per a few chapters later in Genesis, that Sarah was approaching menopause, because, when she was 90, and beyond the time of women, she laughed out loud when the three angels stopped in for lunch, and one had said, she'd have a son.  (1st half of Genesis 18)   So, would make sense to believe, somewhere between 76 and 90, she no longer needed to add kotex (or midol) to her shopping list.

Anyway, it was right after sodom and gomorrah (Genesis 13:10 describes prime real estate) were destroyed - by brimstone and fire from the sky (Genesis 19:24), the couple and company had broken camp, and relocated to a place called Gerar.   Did they need to get away from the brimstony smell?  Was it getting into their water, flour, clothing?  Asking, because the area of sodom had been "well watered" ; so, can only imagine the hot sulfur and steam - yuk.  Abraham, per Genesis 19:28, saw the smoke in the distance, and probably got a whiff - pee-double-uweee :/

Anyway, Abimelech, the king of Gerar, took a fancy to Sarah, and put her in his harem.  Maybe, he had a thing for older women ; or maybe he was simply amazed at how such a woman her age (like early 50s today) could be so good looking.  Kings back then, collected women - sort of like fine paintings, or rare baseball cards.  While i don't know Abimelech's age, am going to guess - just for the sake of what happened later - that the king was a few years younger than Sarah.  Let's say, the king was 80.

Now, forty years later, Sarah's son, Isaac, and her daughter-in-law, Rebekah, had relocated to gerar - because of a famine.  Well guess what!  Abimelech, if it was the same Abimelech - Bible doesn't say son of, or Abimelech, Jr. - happened to look out the window and see the couple smooching (Genesis 26:8).  If it's the same King, then he would have been 120 years old, maybe younger, maybe older, but well up in years, by our standards today.  

All's i know is, Roman's 1:20 basically says, all you have to do is take a look around, to see that God is real.  As for the longer life spans, per the Bible - which is evidence enough, thankyoukindly - evidently, there's something to those old "myths"...about this or that chinese king ruling for a 100 years.  

"Now Abraham and Sarah were old and well stricken in age; and it ceased to be with Sarah after the manner of women."  Genesis 18:11