Question

The perimeter of a rhombus is $52cm$. If one diagonal is $24cm$, find its area.

• A. $110$ sq. cm
• B. $120$ sq.cm
• C. $125$ sq. cm
• D. $130$ sq. cm

Answer 1

The correct option is B $120$ sq.cm

The perimeter of a rhombus is $52cm$
$\Rightarrow 4a=52$
$\Rightarrow a=13cm$

Let the other diagonal be $d$

By Pythagoras Theorem,

$a^2={\left(\frac{24}{2}\right)}^2+{\left(\frac{d}{2}\right)}^2$

$\Rightarrow {\left(\frac{d}{2}\right)}^2={13}^2-{12}^2$

$\Rightarrow {\left(\frac{d}{2}\right)}^2=169-144$

$\Rightarrow {\left(\frac{d}{2}\right)}^2=25$

$\Rightarrow d^2=25\times 4$

$\Rightarrow d=10cm$

Now, area of rhombus $=\frac{d_1{d}_2}{2}$

$=\frac{24\times 10}{2}$

$=120sq.cm$