[btilly]

Perhaps he’d say that such a triangle doesn’t exist physically.

I am certain that this is the case given that he's referring to the maximum information density density of space as one of the reasons why exact numbers make no physical sense. See https://en.wikipedia.org/wiki/Bekenstein_bound if you don't know about that limit.

More directly, the inability to represent exact lengths falls out of the Heisenberg Uncertainty principle. As an abstract mathematical concept, numbers could be anything. As a physically relevant concept, there are limits to how much precision can matter.