Question

The length of the diagonals of a rhombus are $24cm$ and $18cm$. Find the length of each side of the rhombus

Answer 1

Let the rhombus is $ABCD,$ given that :

$AC=24cm$ and $BD=18cm.$

Let the Diagonal of Rhombus bisect each other at right angles.

$AO=OC=$ $12$

and OB = OD =$9$ cm

Let $\angle AOD={90}^{\circ }$

In right $\Delta AOD,$

AO= $12$ cm and OD=$9$ cm

Using phythagoras theorem,

$A{D}^2=A{O}^2+O{D}^2$

$A{D}^2=(12{)}^2+(9{)}^2$

AD=$15$ cm

Hence the all side of rhombus are equal

Hence the each side of the rhombus is $15cm.$