Question

Find the area of a rhombus whose side is 6 cm and whose altitude is 4 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ \mathrm{Side}\mathrm{of}\mathrm{the}\mathrm{rhombus}=6\mathrm{cm} \\ \mathrm{Altitude}=4\mathrm{cm} \\ \mathrm{One}\mathrm{of}\mathrm{the}\mathrm{diagonals}=8\mathrm{cm} \\ \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{rhombus}=\mathrm{Side}\times \mathrm{Altitude}=6\times 4=24{\mathrm{cm}}^2........\left(\mathrm{i}\right) \\ \mathrm{We}\mathrm{know}:\mathrm{Area}\mathrm{of}\mathrm{rhombus}=\frac{1}{2}\times {\mathrm{d}}_1\times {\mathrm{d}}_2 \\ \mathrm{Using}\left(\mathrm{i}\right): \\ 24=\frac{1}{2}\times {\mathrm{d}}_1\times {\mathrm{d}}_2 \\ 24=\frac{1}{2}\times 8\times {\mathrm{d}}_2 \\ {\mathrm{d}}_2=6\mathrm{cm} \end{gathered}$$