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
$\text{In}△AOB$,
$\Rightarrow O{A}^2+O{B}^2=A{B}^2$
$\Rightarrow {10}^2+{10.5}^2=A{B}^2$
$\Rightarrow 100+110.25=A{B}^2$
$\Rightarrow A{B}^2=210.25$
$\Rightarrow AB=14.5cm$
Thus, each side of rhombus = 14.5 cm
Perimeter = AB + BC + CD + DA
$=14.5+14.5+14.5+14.5$
$=58\text{cm.}$