It turns out Petra does not like tomatoes, even though she did eat a carrot two weeks ago. She dropped it after about 15 minutes, and I saw no evidence she had bitten into it. (The coloring is off, because the camera was on the wrong setting.)
I put a baby carrot in Petra's enclosure to lure out the dubia roach that was hiding out of reach. After eating the roach, Petra went for the carrot. To my surprise, she spent over two hours feeding on the carrot, and when she was finished, it was less than half its original size.