Question

If the area of rhombus is 48 cm sq. and one of its diagonals is 12 cm, find the side of the rhombus.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{each}\mathrm{side}\mathrm{of}\mathrm{rhombus}=\mathrm{s}\mathrm{cm} \\ \mathrm{Let}{\mathrm{d}}_1\mathrm{and}{\mathrm{d}}_2\mathrm{be}\mathrm{the}2\mathrm{diagonals}\mathrm{of}\mathrm{rhombus}. \\ \mathrm{Now},{\mathrm{d}}_1=12\mathrm{cm} \\ \mathrm{Now},\mathrm{area}=48{\mathrm{cm}}^2 \\ \Rightarrow \frac{1}{2}\times {\mathrm{d}}_1\times {\mathrm{d}}_2=48 \\ \Rightarrow \frac{1}{2}\times 12\times {\mathrm{d}}_2=48 \\ \Rightarrow {\mathrm{d}}_2=8\mathrm{cm} \\ \mathrm{Now},\mathrm{s}=\sqrt{{\left(\frac{{\mathrm{d}}_1}{2}\right)}^2+{\left(\frac{{\mathrm{d}}_2}{2}\right)}^2} \\ \Rightarrow \mathrm{s}=\sqrt{{\left(\frac{12}{2}\right)}^2+{\left(\frac{8}{2}\right)}^2} \\ \Rightarrow \mathrm{s}=\sqrt{36+16} \\ \Rightarrow \mathrm{s}=\sqrt{52} \\ \Rightarrow \mathrm{s}=2\sqrt{13}\mathrm{cm} \end{gathered}$$