ABCD is a rhombus

AC = 18cm

BD = 24cm

We have to find the sides of the rhombus

In triangle AOB,

AO = 9cm (Diagonals of a parallelogram bisect each other)

BO = 12cm

AOB is a right - triangle right angled at O (Diagonals of a rhombus are perpendicular to each other)

So,

AB² = AO² + BO² (By Pythagoras theorem)

AB² = 9² + 12²

AB² = 81 + 144

AB² = 225

AB = 15cm

In a rhombus, all sides are equal

Thus, each side of the rhombus is 15cm.