Question

The area of a rhombus is $216$ sq. cm. If its one diagonal is $24$ cm; find perimeter of the rhombus.

Answer 1

Area of a rhombus $=\frac{1}{2}\times (diagonal1\times diagonal2)$

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

$=>\frac{1}{2}\times 24\times diagonal2=216{cm}^2$

Hence, 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, triangle POQ is a right angled triangle,
${PQ}^2={OP}^2+{OQ}^2=>9^2+{12}^2=225$
$PQ=\sqrt{225}=15$ cm
Hence, the length of the sides of the diagonal $=15$ cm.
Since the length of all sides of a rhombus are equal, Perimeter $=4\times$ length of one side $=4\times 15=60cm$