Length of diagonals = 6cm and 8cm
Half the diagonals, 3cm and 4cm
The diagonals divide the rhombus in four right angled triangles.
(Since, the diagonals of rhombus intersect at right angles)
So, using Pythagoras theorem,
a²+b² = c²
3²+4² = c²
25 = c²
c = √25
c = 5 cm
So, one side of the rhombus is 5cm.