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Question

The lengths of the diagonals of a rhombus are 24 cm and 18 cm respectively. Find the length of each side of the rhombus.

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Solution

Let ABCD be a rhombus.
∴ AB = BC = CD = DA
Here, AC and BD are the diagonals of ABCD, where AC = 24 cm and BD = 18 cm.
Let the diagonals intersect each other at O.
We know that the diagonals of a rhombus are perpendicular bisectors of each other.
AOBisarightangletriangleinwhichOA=AC2}=242 = 12 cm and OB = BD2=182 = 9 cm.
Now,AB2=OA2+OB2
[Pythagoras theorem]
⇒​ AB2=(12)2+(9)2
⇒​ AB2=144+81=225
⇒​ =15cm
Hence, the side of the rhombus is 15 cm.


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