Question

The area of a rhombus is $216$ $c{m}^2$. If its one diagonal is $24cm$; find the length of its side.

Answer 1

Area of a rhombus $=\frac{1}{2}\times (\text{diagonal 1}\times \text{diagonal 2})$

Given, Area $=216{cm}^2$

$=>\frac{1}{2}\times 24\times \text{diagonal 2}=216{cm}^2$

Hence, $\text{diagonal 2}=18cm$

In a rhombus, the diagonals bisect each other at ${90}^0$
Referring the diagram, if $PR=18cm$, $SQ=24cm$, then $OP=9cm$, $OQ=12cm$
Since, $△POQ$ is a right angled triangle,
${PQ}^2={OP}^2+{OQ}^2=>9^2+{12}^2=225$
$PQ=\sqrt{225}=15cm$
Hence, the length of the sides of the diagonal $=15cm$