Let ABCD be rhombus.

Here, AC and BD are the diagonals of ABCD, where AC = 24 cm and BD = 18 cm.
Let the diagonals intersect each other at O.
We know that the diagonals of a rhombus are perpendicular bisectors of each other.
∴​ ∆AOB is a right angle triangle in which OA = = 12 cm and OB = = 9 cm.
Now, AB²= OA² + OB² …Pythagoras theorem
∴​ AB²=​ (12)² + (9)²
∴​ AB²=​ 144 + 81 = 225
∴​ AB =​ 15 cm
Hence, the side of the rhombus is 15 cm