Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
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)$1: \sqrt{2}$
Answer
Answer (as printed): D
Explanation
Let the length of diagonal of the bigger square be $x$ and that of the smaller square be $y$. Then, $A=\frac{1}{2} x^{2} \quad$ or $\quad x=\sqrt{2 A}$. And, $\frac{A}{2}=\frac{1}{2} y^{2} \quad$ or $\quad y=\sqrt{A}$. $$\therefore \quad \text { Required ratio }=\frac{y}{x}=\frac{\sqrt{A}}{\sqrt{2 A}}=1: \sqrt{2} .$$
Explanation as extracted from the printed page; notation may be imperfect.