“You don't know how strong something is until you actually test it.”

Source: The Rose That Grew from Concrete

Source: Tuesdays with Morrie

Variant: No one cares how much you know, until they know how much you care

Another quote often attributed to her without an original source in her writings, as in The Wit and Wisdom of Eleanor Roosevelt (1996), p. 199. But once again archivists have not been able to find the quote in any of her writings, see the comment from Ralph Keyes in The Quote Verifier above.
A very similar remark was attributed to Nancy Reagan, in The Observer (29 March 1981): "A woman is like a teabag — only in hot water do you realize how strong she is."
Variants:
A woman is like a teabag. You never know how strong she is until she gets into hot water.
A woman is like a tea bag, you can not tell how strong she is until you put her in hot water.
A woman is like a tea bag; you can't tell how strong she is and how much to trust her until you put her in hot water.
Disputed

Source: Fried Green Tomatoes at the Whistle Stop Cafe

Source: Halliwell, Leslie, Halliwell's Who's Who in the Movies http://books.google.com/books?id=cnMelOEV10YC, 4th ed. (2006) HarperCollins

Source: Rework