Question

$ABCD$ is a rhombus. If $AC=6$ cm and $BD=9$ cm. Then, find perimeter of rhombus $ABCD$.

Answer 1

Diagonals of rhombus perpendicular bisect each other $=AO=3cm$, $OB=4.5$cm

By Pythagoras theorem, $a^2=O{A}^2+O{B}^2=9+\frac{81}{4}$

$\Rightarrow a^2=\frac{36+81}{4}=\frac{117}{4}$

$\Rightarrow a=\frac{3\sqrt{13}}{2}$

$\Rightarrow$ Perimeter $=4a=6\sqrt{13}$cm.