Question

In the given rhombus ABCD,If the length of diagonals of rhombus are 8 cm and 6 cm, then the side of the rhombus is .

• A. 3 cm
• B. 6 cm
• C. 4 cm
• D. 5 cm

Answer 1

The correct option is D 5 cm

In the figure,

AC and BD are the diagonals of rhombus ABCD.
Diagonals of a rhombus are perpendicular and bisect each other.
So, OA = OC = $\frac{1}{2}$AC = 4 cm
OB = OD = $\frac{1}{2}$BD = 3 cm
and $\angle AOB=90°$
Using Pythagoras theorem,
$O{A}^2+O{B}^2=A{B}^2$
$A{B}^2=3^2+4^2$
AB = 5 cm.

Hence, the side of rhombus ABCD is 5 cm.