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