Question

The perimeter of rhombus is $52$ sq. cm. If one of its diagonal is $24cm$; find the length of its other diagonal.

Answer 1

The perimeter of a rhombus is $52cm$
$\Rightarrow 4a=52$
$\Rightarrow a=13cm$
Let the length of other diagonal be $d$
$\therefore a^2={\left(\frac{24}{2}\right)}^2+{\left(\frac{d}{2}\right)}^2$
$\Rightarrow {\left(\frac{d}{2}\right)}^2={13}^2-{12}^2$
$\Rightarrow {\left(\frac{d}{2}\right)}^2=169-144$
$\Rightarrow {\left(\frac{d}{2}\right)}^2=25$
$\Rightarrow d^2=25\times 4$
$\Rightarrow d=10cm$