HAVERFORD, Pa. — The teenager leaned into the microphone, pausing for a beat. She had a question for Hillary Clinton, about her high school and Donald J. Trump.

“At my school, body image is a really big issue for girls my age,” began the girl, Brennan Leach, 15, who had a red bow in her hair. “I see with my own eyes the damage Donald Trump does when he talks about women and how they look.”

How, she asked, could Mrs. Clinton help girls understand “that they are so much more than just what they look like?”

Briefly, Mrs. Clinton appeared ready to rocket out of her seat.

“Thank you!” the candidate shouted, as the crowd cheered Brennan. “Thank you!”