Find the length o

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