If a square of area A2 is cut off from a given square of area A, then the ratio of diagonal of the cut off square to that of the given square is :

Answer: Option D

Let the length of diagonal of the bigger square be x and that of the smaller square be y.
Then,
$$A=\frac{1}{2}{x}^{2}orx=\sqrt{2A}$$
And,
$$\frac{A}{2}=\frac{1}{2}{y}^{2}ory=\sqrt{A}$$
$$\begin{array}{rl}& \therefore \text{ Required ratio :}\\ & =\frac{y}{x}=\frac{\sqrt{A}}{\sqrt{2A}}=1:\sqrt{2}\end{array}$$