Q19 of 95 Page 5

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


⇒ (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.


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