Question

In the given figure, ABCD is a rhombus where $BO=12cm$ and $OC=5cm$. find the values of $x,y$ and $z$

Answer 1

In a rhombus, diagonals are perpendicular to each other and bisect each other.

$\therefore BO=OD=12cm$

$\therefore y=12cm$

and

$CO=OA=5cm$

$\therefore x=5cm$

Since ${BC}^2={CO}^2+{BO}^2$, by substituting values we get:

${BC}^2=(12{)}^2+{\left(5\right)}^2$

$\Rightarrow BC=\sqrt{169}$

$\Rightarrow BC=13cm$

Since all sides are equal, BC=CD

$\therefore z=13cm$

Hence, the value of x is 5cm and the value of z is 13cm.