# Find the length of the second diagonal of a rhombus, whose side is 5 cm and one of the diagonals is 6 cm. 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

(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.

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