Question

In the given figure, $ABCD$ is a rhombus, find the values of $x,y$ and $z$

Answer 1

From the figure,$ABCD$ is a rhombus
Then, the diagonals of rhombus bisect each other at right angles.
$So,AO=OC$
$x=8cm$
Therefore, $AO=8cm$
And $BO=OD$
$y=6cm$
Therefore, $BO=6cm$
Consider the $\Delta AOB$, it is a right angled triangle.
By Pythagoras theorem,
${AB}^2={AO}^2+{BO}^2$
${AB}^2=8^2+6^2$
${AB}^2=64+36$
${AB}^2=100$
$AB=\sqrt{100}$
$AB=10cm$