Answer :

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.

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