Answer: The word that best completes the sentence is "youthful".
Explanation: The word "youthful" is an adjective and it is generally used to refer to someone that is/seems young or has the attitude that a young person would have. The use of "youthful" in the sentence provided is coherent because the speaker is referring to someone that is old ("a woman in her seventies"), but looks young. In contrast, "childish" and "childlike" denote other meanings: they are generally used to characterize someone as a child.