I remember way back in high school there were two standards for doing push-ups: one for the boys and one for the girls.
For the boys it was the form we usually think of, that is, body straight, only toes and hands touching the floor, go from there.
But the girls were allowed to be down on hands and knees, and in that position do their push-ups, hands and knees constantly in contact with the floor.
Maybe that was reasonable, I don't know, and I don't know if the schools still do it that way.
But if you really
want to talk about real push-ups
, one need only consult the true masters of the exercise, Marine Corps troops:https://www.youtube.com/watch?v=fxiqe4vvhmi
(And the troops doing them while chanting "One-two-three-four, I love the Marine Corps!")