Question

The diagonals of a rhombus are $12cm$ and $6cm$. Find the length of side of the rhombus.

• A. $\sqrt{5}$
• B. $2\sqrt{5}$
• C. $3\sqrt{5}$
• D. $4\sqrt{5}$

Answer 1

The correct option is C $3\sqrt{5}$

We know that diagonals of a rhombus perpendicularly bisect each other.

Therefore

Let side of rhombus be 'a' , then

$a^2={\left(\frac{d_1}{2}\right)}^2+{\left(\frac{d_2}{2}\right)}^2={\left(\frac{12}{2}\right)}^2+{\left(\frac{6}{2}\right)}^2=36+9$

$a^2=45\Rightarrow a=3\sqrt{5}$