Question

The area of a rhombus is 144 cm² and one of its diagonals is double the other. The length of the
longer diagonal is

(a) 12 cm (b) 16 cm (c) 18 cm (d) 24 cm

Answer 1

Let d₁ and d₂ be the diagonals of the rhombus, where d₁ = 2d₂.
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{rhombus}=\frac{1}{2}\times d_1\times d_2 \\ \Rightarrow 144=\frac{1}{2}\times d_1\times \frac{d_1}{2}\left(\because d_1=2d_2\right) \\ \Rightarrow {d_1}^2=4\times 144 \\ \Rightarrow d_1=2\times 12=24\mathrm{cm} \end{gathered}$$
Hence, the correct option is (d).