Question

If the area of a rhombus is 96 $c{m}^2$ and one of its diagonals is 12 cm, find its perimeter.

Answer 1

$P\left(Diagonal\right)=12cm$

$A\left(Area\right)=96c{m}^2$

Using the formula

$A=\frac{Pq}{2}$

$q=4a$

$a=\frac{\sqrt{P^2+q^2}}{2}$

$P=\sqrt{2P^2+4{\left(\frac{A}{P}\right)}^2}=2\sqrt{{12}^2+4{\left(\frac{96}{12}\right)}^2}=40cm.$

Hence, this is the answer.