Question

The length of a diagonal of a rhombus is 16 cm. If its area is 96 cm², then the length of other
diagonal is

(a) 6 cm (b) 8 cm (c) 12 cm (d) 18 cm

Answer 1

Let d₁ and d₂ be the diagonals of the rhombus, where d₁ = 16 and area of rhombus = 96 cm².
Area of parallelogram = $\frac{\text{1}}{\text{2}}\left(d_1\times d_2\right)$
$$\begin{gathered} \Rightarrow 96=\frac{\text{1}}{\text{2}}\left(16\times d_2\right) \\ \Rightarrow d_2=\frac{96\times 2}{16}=12\mathrm{cm} \end{gathered}$$
Thus, the length of other diagonal is 12 cm.
Hence, the correct option is (c).