You can't fit 100 perfect squares into an area that is 25 by 39 units. 25 times 39 is 975 square units, so each of the 100 squares would have to measure 9.75 square units in area. Then each side of the 100 squares would be sqrt(9.75). sqrt(9.75) is an irrational number that does not evenly divide 25 or 39.
John
My calculator said it, I believe it, that settles it