Question

If the lengths of the diagonals of the rhombus are $16\mathrm{cm}$ and $12\mathrm{cm}$. Then, the length of the sides of the rhombus is

• A. $9\mathrm{cm}$
• B. $10\mathrm{cm}$
• C. $8\mathrm{cm}$
• D. $20\mathrm{cm}$

Answer 1

The correct option is B

$10\mathrm{cm}$

The explanation for the correct answer.

Find the length of the rhombus:

Given: Length of diagonal of $\mathrm{AC}=16\mathrm{cm}\mathrm{and}\mathrm{BD}=12\mathrm{cm}$

Diagonal of a rhombus are perpendicular bisectors of each other.

$\therefore \mathrm{AO}=8\mathrm{cm}\mathrm{and}\mathrm{BO}=6\mathrm{cm}$

$$\begin{gathered} Also\angle \mathrm{AOB}=90° \\ \Rightarrow {\mathrm{AB}}^2={\mathrm{AO}}^2+{\mathrm{BO}}^2[\mathrm{Pythagoras}\mathrm{Theorem}] \\ \Rightarrow \mathrm{AB}=\sqrt{{\mathrm{AO}}^2+{\mathrm{BO}}^2} \\ \Rightarrow \mathrm{AB}=\sqrt{{\left(8\right)}^2+{\left(6\right)}^2}[\mathrm{AO}=8\mathrm{cm}\mathrm{and}\mathrm{BO}=6\mathrm{cm}] \\ \Rightarrow \mathrm{AB}=\sqrt{64+36} \\ \Rightarrow \mathrm{AB}=\sqrt{100} \\ \Rightarrow \mathrm{AB}=10\mathrm{cm} \end{gathered}$$

Therefore the length of the sides of the rhombus $=10\mathrm{cm}$.

Hence option (b) is the correct answer.