question_answer 1)

                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:

                Area of the rhombus = base \[\times \] altitude \[=6\times 4\,=24\,c{{m}^{2}}\] Area of the rhombus \[=\frac{1}{2}\,\times {{d}_{1}}\times {{d}_{2}}\] \[\Rightarrow \]               \[24=\frac{1}{2}\times 8\times {{d}_{2}}\] \[\Rightarrow \]               \[24=4\,{{d}_{2}}\] \[\Rightarrow \]               \[{{d}_{2}}=\frac{24}{4}\,=6\,cm\] Hence, the length of the other diagonal is 6 cm.