If a square of area $$\frac{\text{A}}{2}$$ 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 :

Solution (By Examveda Team)

Let the length of diagonal of the bigger square be x and that of the smaller square be y.
Then,
$$A = \frac{1}{2}{x^2}\,\,or\,\,x = \sqrt {2A} $$
And,
$$\frac{A}{2} = \frac{1}{2}{y^2}\,\,or\,\,y = \sqrt A $$
$$\eqalign{ & \therefore {\text{ Required ratio :}} \cr & = \frac{y}{x} = \frac{{\sqrt A }}{{\sqrt {2A} }} = 1:\sqrt 2 {\text{ }} \cr} $$