You made me go back and look at the Nova/PBS video "Why the Towers Fell." I obviously shouldn't depend on my memory. The TV tower was on the north building. It started dropping first, indicating that the core failed first. The south building's outer wall fails first (due to fire-weakened floor supports), while its core resists the collapse. (I got the failure reasons right.)
Leslie Robertson was the lead structural engineer on the project. He designed, ". . . for the impact of the largest plane of its time, a Boeing 707."
Both buildings survived the impacts:
8:46 AM North Tower Hit,
9:03 AM South Tower Hit,
9:59 AM South Tower Falls,
10:28 AM North Tower Falls.
The South Tower lasted 56 minutes.
The North Tower lasted 1 hour 42 minutes.
Strengthen Fire Resistance,
Provide Back-Up Supports.
To quote Jonathan Barnett, an expert on fire protection, "In fact, until 9-11, I was unaware of any protected steel structure that had collapsed any where in the world from just a fire."