A rod was cut into three pieces. The lengths of the three pieces are in the ratio 5:3:2. If the shortest is 25cm long how was the rod?
Let the common ratio between the lengths of the three pieces be "x."
Therefore, the lengths of the three pieces are 5x, 3x, and 2x.
Given that the shortest piece is 25 cm long, we have:
2x = 25
x = 25/2
x = 12.5
So, the lengths of the three pieces are 5x = 5(12.5) = 62.5 cm, 3x = 3(12.5) = 37.5 cm, and 2x = 2(12.5) = 25 cm.
Therefore, the rod was 62.5 + 37.5 + 25 = <<62.5+37.5+25=125>>125 cm long. Answer: \boxed{125}.