Erich Friedman has collected solutions and notes:
All of these are probably optimal, except for possibly n=20.
But by adding the domino areas, one gets:
So the side length must be at least $\lceil\sqrt A\rceil=76$, as given. Is it really that simple or have I misunderstood something?
What (better) lower and upper bound can be given for the general case of $n$ consecutive dominoes?
Edit: Ah, it does not say anywhere that the sides of the dominoes have to be parallel to a side of the square. So I have no proof that the solution is optimal. Got it.