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

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{BD}=20\mathrm{cm} \\ \Rightarrow \mathrm{BO}=\frac{\mathrm{BD}}{2}=\frac{20}{2}=10\mathrm{cm} \\ \mathrm{As},\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{rhombus}\mathrm{ABCD}=480{\mathrm{cm}}^2 \\ \Rightarrow \frac{1}{2}\times \mathrm{AC}\times \mathrm{BD}=480 \\ \Rightarrow \frac{1}{2}\times \mathrm{AC}\times 20=480 \\ \Rightarrow \mathrm{AC}\times 10=480 \\ \Rightarrow \mathrm{AC}=\frac{480}{10} \\ \Rightarrow \mathrm{AC}=48\mathrm{cm} \\ \Rightarrow \mathrm{AO}=\frac{\mathrm{AC}}{2}=\frac{48}{2}=24\mathrm{cm} \\ \mathrm{Now},\mathrm{in}∆\mathrm{AOB}, \\ \mathrm{Using}\mathrm{Pythagoras}\mathrm{theorem}, \\ {\mathrm{AB}}^2={\mathrm{AO}}^2+{\mathrm{BO}}^2 \\ ={24}^2+{10}^2 \\ =576+100 \\ \Rightarrow {\mathrm{AB}}^2=676 \\ \Rightarrow \mathrm{AB}=\sqrt{676} \\ \therefore \mathrm{AB}=26\mathrm{cm} \end{gathered}$$

Hence, the correct answer is option (c).