Question

Diagonals of a rhombus are 20 cm and 21 cm respectively, then find the side of rhombus and its perimeter.

Answer 1

Let ABCD be the rhombus.
AC = 20 cm and BD = 21 cm
We know that the diagonals of a rhombus bisect at right angles.
So, AO = OC = 10 cm
And BO = OD = 10.5 cm
In $△$AOB,
$$\begin{gathered} {\mathrm{AO}}^2+{\mathrm{OB}}^2={\mathrm{AB}}^2 \\ \Rightarrow {10}^2+10.5^2={\mathrm{AB}}^2 \\ \Rightarrow 100+110.25={\mathrm{AB}}^2 \\ \Rightarrow {\mathrm{AB}}^2=210.25 \\ \Rightarrow \mathrm{AB}=14.5\mathrm{cm} \end{gathered}$$
Thus, each side of rhombus = 14.5 cm
Perimeter = AB + BC + CD + DA = 14.5 + 14.5 + 14.5 + 14.5 = 58 cm.