Question

If perimeter of a Rhombus is $100cm$ and length of one diagonal is $48cm$, what is the area of the Rhombus?

Answer 1

Perimeter of rhombus of side $a=4a$

$\Rightarrow 4a=100$

$\Rightarrow a=25$cm.

Let $AC=48$cm

As diagonals bisect each other in rhombus

$\Rightarrow AO=24cm$

By Pythagoras theorem in $\Delta$AOD, $A{D}^2=A{O}^2+O{D}^2$

$\Rightarrow O{D}^2=\sqrt{625-576}=\sqrt{49}=7cm$

$\Rightarrow BD=14$cm

Area $=\frac{1}{2}{d}_1{d}_2=\frac{1}{2}\left(14\right)\left(48\right)=7\times 48=336c{m}^2$.