The diagonals of a rhombus are perpendicular bisectors of each other. 

This means that they divide the rhombus into four right triangles, each with legs of length half the length of the diagonals. 

In this case, the legs of each right triangle are 3 cm and 4 cm long. 

By the Pythagorean theorem, the length of the hypotenuse of each right triangle, which is also the length of a side of the rhombus, is \(\sqrt{3^2 + 4^2} = 5\) cm. 

Therefore, the length of a side of the rhombus is 5 cm.