Question

The ratio of the areas of two squares, one having its diagonal double that of the other, is

(a) 2 : 1 (b) 3 : 1 (c) 3 : 2 (d) 4 : 1

Answer 1

Let d be the diagonal of the second square. Then, the diagonal of the first square will be 2d.
∵ $\mathrm{Side}\mathrm{of}\mathrm{a}\mathrm{square}=\frac{\mathrm{Diagonal}}{\sqrt{2}}$
∴ $\mathrm{Required}\mathrm{ratio}=\frac{{\left({\displaystyle \frac{2d}{\sqrt{2}}}\right)}^2}{{\left({\displaystyle \frac{d}{\sqrt{2}}}\right)}^2}=\frac{2d^2}{{\displaystyle \frac{{\displaystyle d^2}}{{\displaystyle 2}}}}=4:1$
Hence, the correct option is (d).