Question

Diagonals of a rhombus are $8cm,6cm$ respectively. Its side is-

• A. $5cm$
• B. $6cm$
• C. $7cm$
• D. cannot be determined

Answer 1

The correct option is A $5cm$

Let $ABCD$ is rhombus, $AC$ and $BD$ are diagonals.

$AC=8cm$ and $BD=6cm$

We know that diagonals of rhombus perpendicularly bisect each other.

$\therefore$ $AO=\frac{AC}{2}=\frac{8}{2}=4cm$

$\Rightarrow$ $BO=\frac{6}{2}=3cm$

In right angles $△AOB,$

$\Rightarrow$ $(AB{)}^2=(AO{)}^2+(BO{)}^2$

$\Rightarrow$ $(AB{)}^2=(4{)}^2+(3{)}^2$

$\Rightarrow$ $(AB{)}^2=16+9$

$\Rightarrow$ $(AB{)}^2=25$

$\therefore$ $AB=5cm$

$\Rightarrow$ $AB=BC=CD=DA=5cm$ [ In rhombus all sides are equal. ]