Question

The lengths of the diagonals of a Rhombus are $12cm$ and $16cm$. Find the side of the rhombus

Answer 1

Since the diagonals of a rhombus bisect each other at right angles
$\begin{array}{cc}& AO=\frac{1}{2}AC=\frac{1}{2}\times 12=6cm\\ & BO=\frac{1}{2}BD=\frac{1}{2}\times 16=8cm\end{array}$
In the right triangle $AOD$
$\begin{array}{cc}& {AD}^2={AO}^2+{DO}^2\\ & =6^2+8^2\\ & =36+64\\ & =100\\ & \therefore AD=\sqrt{100}\\ & =10\\ & \therefore AB=BC=CD=AD=10cm\end{array}$