$ \mathrm{RACE} $ is a rhombus, as shown. Find the values

of $ x, y $ and $ z $.
"

Given: $RACE$ is a rhombus, as shown in the figure.

To do: To find $x,\ y$ and $z$.

Solution:

$\because RACE$ is a rhombus.

$\therefore$ Diagonals $RC$ and $AE$ bisects each other at $90^o$.

$\Rightarrow OC=OR$ and $OA=OE$

$\Rightarrow y=12\ cm$ and $x=9\ cm$

In right angled $\vartriangle AOC$, on using Pythagoras theorem,

$z^2=x^2+y^2$

$\Rightarrow z^2=9^2+12^2$

$\Rightarrow z^2=81+144$

$\Rightarrow z^2=225$

$\Rightarrow z=\sqrt{225}$

$\Rightarrow z=15\ cm$

Thus, $x=9\ cm, y=12\ cm$ and $z=15\ cm$.

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Updated on: 10-Oct-2022

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