Let ABCD be a rhombus having AD = 5cm and AC = 6cm
Now, we know that diagonals of rhombus bisect each other at 90°
Thus, we have
Since, AOD is a right angled triangle
So, by Pythagoras theorem, we have
(Perpendicular)2 + (Base)2 = (Hypotenuse)2
⇒ (AO)2 + (BO)2 = (AD)2
⇒ (3)2 + (BO)2 = (5)2
⇒ (BO)2 = 25 – 9
⇒ (BO)2 = 16
⇒ BO = √16
⇒ BO = ±4
⇒ BO = 4 [taking positive square root]
Hence, BO = 4cm
⇒ BC = 2BO = 2 × 4 = 8cm
Thus, length of each side of rhombus is 13cm.
