Q. 11

# 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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