Question

The area of an $A_0$ paper is one square metre. What are the lengths of the sides of an $A_3$ paper ? (answer in millimetres)

• A. 480.382, 297.3
• B. 296.32, 210
• C. 296.4, 148.49
• D. 420, 210

Answer 1

The correct option is A

480.382, 297.3

Given $A0=1m^2$

We know that the ratio of $A0$ to $A3$ is 8:1.
$\frac{A0}{A3}=\frac{8}{1}$
$\frac{1}{A3}=\frac{8}{1}$
$A3=\frac{1}{8}{m}^2$
Let the length of the $A3$ paper be $x$ and breadth be $y$ respectively.

The length of an $A3$ paper is $\sqrt{2}$ times its breadth.
i.e., $x=\sqrt{2}y$ ...(i)
Also, $A3=x\times y$
$⟹\frac{1}{8}=\sqrt{2}y\times y$ (From eqn. (i))
$⟹y^2=\frac{1}{8\sqrt{2}}$
$⟹y^2=\frac{\sqrt{2}}{8\times 2}$
$⟹y^2=\frac{\sqrt{2}}{16}=0.0883883$
$⟹y=0.2973m=297.3mm$
Now $x=\sqrt{2}\times y$ implies $x=1.414\times 297.3=420.382mm$