Question

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

• A. 60 cm
• B. 80 cm
• C. 100 cm
• D. 120 cm

Answer 1

The correct option is A 60 cm

Since,

Area of rhombus$=\frac{1}{2}\times d1\times d2$

$\Rightarrow 216=\frac{1}{2}\times 24\times d2$

$\Rightarrow 216=12\times d2$

$\Rightarrow \frac{216}{12}=d2$

$\Rightarrow d2=18cm$

So, second diagonal $=18cm$

As shown in fig. $AC=18CM,BD=24CM$

Since, diagonals of rhombus bisects each other at right angle.
$\therefore AO=9cm,DO=12cm$

In $△AOD$
$A{O}^2+D{O}^2=A{D}^2$
$\Rightarrow 9^2+{12}^2=A{D}^2$
$\Rightarrow 81+144=A{D}^2$
$\Rightarrow 225=A{D}^2$
$\Rightarrow AD=15cm$

$\therefore$ side of rhombus $\left(AD\right)=15cm$

Perimeter of rhombus $=4\times side$
$=4\times 15=60cm$

Perimeter of rhombus $=60cm$