Q11 of 95 Page 5

Find the length of each side of a rhombus whose diagonals are 24 cm and 10 cm long.


Let ABCD be a rhombus where AC = 10cm and BD =24cm


Let AC and BD intersect each other at O.


Now, we know that diagonals of rhombus bisect each other at 90°


Thus, we have




Since, AOB is a right angled triangle


So, by Pythagoras theorem, we have


(Perpendicular)2 + (Base)2 = (Hypotenuse)2


⇒ (AO)2 + (BO)2 = (AB)2


⇒ (5)2 + (12)2 = (AB)2


⇒ (AB)2 = 25 + 144


⇒ (AB)2 = 169


⇒ AB = √169


⇒ AB = ±13


⇒ AB = 13 [taking positive square root]


Hence, AB = 13cm


Thus, length of each side of rhombus is 13cm


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