Question

A rhombus has one diagonal double the other. If the area of rhombus is $kc{m}^2$. then the length of its side is

• A. $\frac{5\sqrt{k}}{4}cm$
• B. $\frac{\sqrt{5k}}{4}cm$
• C. $\sqrt{\frac{5k}{4}}cm$
• D. $\frac{k\sqrt{5}}{4}$

Answer 1

The correct option is C $\sqrt{\frac{5k}{4}}cm$

Let the length of one diagonal be $a$,

The length of other diagonal will be $2a$

We know,

Area of Rhombus$=\frac{1}{2}{d}_1\times d_2$

$=\frac{1}{2}a\times 2a=k$

$=a=\sqrt{k}$ ----(i)

As diagonals intersect each other at right angles,

Let the side of rhombus be $p$

Now,

$p^2={\frac{d_1}{2}}^2+{\frac{d_2}{2}}^2$ -- Pythagoras Theorem.

$p^2=\frac{a^2}{4}+a^2=\frac{5a^2}{4}$

$p=\sqrt{\frac{5a^2}{4}}$

$p=\sqrt{\frac{5k}{4}}$ by (i)

Hence option $\text{C}$ is correct answer.