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.

Answer 1

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.
$\therefore \angle AOBisarightangletriangleinwhichOA=\frac{AC}{2}\}=\frac{24}{2}$ = 12 cm and OB = $\frac{BD}{2}=\frac{18}{2}$ = 9 cm.
Now,$A{B}^2=O{A}^2+O{B}^2$
[Pythagoras theorem]
⇒​ $A{B}^2=(12{)}^2+(9{)}^2$
⇒​ $A{B}^2=144+81=225$
⇒​ $=15cm$
Hence, the side of the rhombus is 15 cm.