Question

The area of a rhombus is $96c{m}^2.$ If one of its diagonals is 16 cm, then the length of its sides is :

• A. $12$ cm
• B. $10$ cm
• C. $8$ cm
• D. $6$ cm

Answer 1

The correct option is B $10$ cm

$\Rightarrow$ We have given area of rhombus = $96c{m}^2$ and $d_1=16cm$.

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

$\Rightarrow$ $96=\frac{1}{2}\times 16\times d_2.$

$\therefore$ $d_2=12cm$

$\Rightarrow$ In given figure ABCD is a rhombus.

$\Rightarrow$ Let $d_1=AC=16cm$ and $d_2=BD=12cm$

$\Rightarrow$ We know that diagonals of rhombus perpendicularly bisect each other.

$\Rightarrow$ So, $AO=8cm$ and $DO=6cm$ --- ( 1 )

$\Rightarrow$ In $△$AOD,

$\Rightarrow$ $A{D}^2=A{O}^2+D{O}^2$ [By using Pythagoras theorem]

$\Rightarrow$ $A{D}^2=8^2+6^2$ [From (1)]

$\Rightarrow$ $A{D}^2=64+36$

$\Rightarrow$ $A{D}^2=100$

$\therefore$ $AD=10cm$

Hence, we get length of sides of rhombus is $10cm.$