# Choose the correct answer of the following question:

Question:

Choose the correct answer of the following question:

The area of a rhombus is 480 cm2 and the length of one of its diagonals is 20 cm. The length of each side of the rhombus is

(a) 24 cm                    (b) 30 cm                    (c) 26 cm                    (d) 28 cm

Solution:

We have,

$\mathrm{BD}=20 \mathrm{~cm}$

$\Rightarrow \mathrm{BO}=\frac{\mathrm{BD}}{2}=\frac{20}{2}=10 \mathrm{~cm}$

As, area of the rhombus $A B C D=480 \mathrm{~cm}^{2}$

$\Rightarrow \frac{1}{2} \times \mathrm{AC} \times \mathrm{BD}=480$

$\Rightarrow \frac{1}{2} \times \mathrm{AC} \times 20=480$

$\Rightarrow \mathrm{AC} \times 10=480$

$\Rightarrow \mathrm{AC}=\frac{480}{10}$

$\Rightarrow \mathrm{AC}=48 \mathrm{~cm}$

$\Rightarrow \mathrm{AO}=\frac{\mathrm{AC}}{2}=\frac{48}{2}=24 \mathrm{~cm}$

Now, in $\triangle \mathrm{AOB}$,

Using Pythagoras theorem,

$\mathrm{AB}^{2}=\mathrm{AO}^{2}+\mathrm{BO}^{2}$

$=24^{2}+10^{2}$

$=576+100$

$\Rightarrow \mathrm{AB}^{2}=676$

$\Rightarrow \mathrm{AB}=\sqrt{676}$

$\therefore \mathrm{AB}=26 \mathrm{~cm}$

Hence, the correct answer is option (c).