Question

If the area of a rhombus is $48c{m}^2$ and one of its diagonals is $12cm$, find the side of the rhombus

• A. $2\sqrt{13}c{m}^2$
• B. $5\sqrt{13}c{m}^2$
• C. $7\sqrt{13}c{m}^2$
• D. $\sqrt{13}c{m}^2$

Answer 1

The correct option is A $2\sqrt{13}c{m}^2$

Let length of each side of rhombus$=xcm$

Let $d_1$ and $d_2$ be the two diagonals of rhombus

Now,

$d_1=12cm$

$Area=48c{m}^2$

We know

Area of rhombus$=\frac{1}{2}\times d_1\times d_2$

$48=\frac{1}{2}\times 12\times d_2$

$d_2=8cm$

Now,

$x=\sqrt{{\left(\frac{d_1}{2}\right)}^2+{\left(\frac{d_2}{2}\right)}^2}$

$x=\sqrt{{\left(\frac{12}{2}\right)}^2+{\left(\frac{8}{2}\right)}^2}$

$x=\sqrt{6^2+4^2}$

$x=\sqrt{36+16}$

$x=\sqrt{52}$

$x=2\sqrt{13}cm$

Therefore length of each side of rhombus is $2\sqrt{13}cm$