# Choose the correct answer of the following question:

Question:

Choose the correct answer of the following question:

One side of a rhombus is 20 cm long and one of its diagonals measures 24 cm. The area of the rhombus is

(a) 192 cm2                    (b) 480 cm2                    (c) 240 cm2                    (d) 384 cm2

Solution:

WE have,

$\mathrm{AB}=\mathrm{BC}=\mathrm{CD}=\mathrm{DA}=20 \mathrm{~cm}$ and $\mathrm{BD}=24 \mathrm{~cm}$

Also, $\mathrm{BO}=\frac{\mathrm{BD}}{2}=\frac{24}{2}=12 \mathrm{~cm}$

In $\Delta \mathrm{AOB}$,

Using Pythagoras theorem

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

$=20^{2}-12^{2}$

$=400-144$

$\Rightarrow \mathrm{AO}^{2}=256$

$\Rightarrow \mathrm{AO}=\sqrt{256}$

$\Rightarrow \mathrm{AO}=16 \mathrm{~cm}$

$\Rightarrow \mathrm{AC}=2 \mathrm{AO}=2 \times 16=32 \mathrm{~cm}$

Now, the area of the rhombus $\mathrm{ABCD}=\frac{1}{2} \times \mathrm{AC} \times \mathrm{BD}$

$=\frac{1}{2} \times 32 \times 24$

$=384 \mathrm{~cm}^{2}$

Hence, the correct answer is option (d).