Question 1017298
If the tile cannot be cut and it's a square, then the largest tile is necessarily 12' with a section of 2x12 left untiled.  However, if the full floor must be tiled with none left over, then:
We know that the tiles must be 1', 2', 3', 4', 6', or 12' (what goes into 12)
Which of these also go into 38"?  Only 1 and 2.  Therefore the largest square tile is 2'.
6 - 2' tiles across, 19 rows of 2' down