Given: Length of one of the diagonals = 24 cm
Length of the other diagonal = 10 cm
To find: Length of the side of the rhombus
∵ The length of all sides of rhombus is equal.
∴ Let side of rhombus ABCD be x cm.
Also, we know that the diagonals of a rhombus are perpendicular bisectors of each other.
⇒ AO = OC = 12 cm and BO = OD = 5 cm
Also, ∠AOB = ∠BOC = ∠COD = ∠AOD = 90°
Now, consider ∆ AOD
AO = 12 cm and OD = 5 cm
∠AOD = 90°
So, using Pythagoras theorem, we have
AD2 = AO2 + OD2 = 122 + 52 = 144 + 25 = 169
⇒ AD = √169 = 13 cm
Rate this question :