Practice | Hashtable

Home > Practice > Arithmetic Aptitude > Area > Miscellaneous

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

A. 1 : 5

B. 1 : $2 \sqrt{5}$

C. 1 : $\sqrt{5}$

D. 1 : $\sqrt{2}$

Solution:

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} o r x = \sqrt{2 A}

And,

\frac{A}{2} = \frac{1}{2} y^{2} o r y = \sqrt{A}

\begin{aligned} ∴ Required ratio : \\ = \frac{y}{x} = \frac{\sqrt{A}}{\sqrt{2 A}} = 1 : \sqrt{2} \end{aligned}

You must login to add comments. Login now.