Question

The two diagonals of a rhombus are 6 units and 8 units.The dimension of each side of the rhombus is units.

Answer 1

Properties of rhombus:

• All sides are equal in length.
• Opposite angles are equal.
• Diagonals bisect each other at ${90}^o.$

Consider the rhombus ABCD.
Given: $AC=8\text{units},BD=6\text{units}$

From the properties of rhombus,
$EC=\frac{AC}{2}=\frac{8}{2}=4\text{units}$
$EB=\frac{DB}{2}=\frac{6}{2}=3\text{units}$

EC and EB are perpendicular.
For $△BCE,BC$ is the hypotenuse.
$\therefore B{C}^2=E{C}^2+E{B}^2$
$\Rightarrow B{C}^2=4^2+3^2=5^2$
$\Rightarrow BC=5\text{units}$

Hence, the dimension of each side of the rhombus is $5\text{units}.$