From the bounding rectangle of the sprite, you can infer the height of a rhombus that fits inside, but you cannot precisely determine the two dimensions on the floor, as each dimension contributes equally to width and height of the sprite. However, if you assume that the base of the rhombus square then you can determine the length of its side as well.
If the sprite is W
pixels wide and H
pixels high, the square base of the rhombus has a side of W / sqrt(3)
and the height of the rhombus will be H - (W / sqrt(3))
. This image of some shapes in isometric projection can be helpful to understand why these formulas work.