ISO standard A4 paper is commonly used throughout most of the world, except in the United States...

Question:

ISO standard A4 paper is commonly used throughout most of the world, except in the United States and Canada. Its dimensions are 210 by 297 mm. This is not a golden rectangle, but the aspect ratio is close to another familiar irrational mathematical quantity. What is that quantity? If you fold a piece of A4 paper in half, what is the aspect ratio of each of the halves?

Aspect Ratio of a Rectangle

The aspect ratio describes the proportion between the lengths of a geometric shape. It may be expressed in the form a:b, in fraction form, or in decimal form.

For a rectangle, the aspect ratio is the ratio of it width to it height.

Answer and Explanation:

The aspect ratio is the ratio of the width to the height. For the case of A4 paper, the aspect ratio is

{eq}\dfrac{297 \text{ mm}}{210 \text{ mm}} = \dfrac{99}{70} \approx \boxed{1.414285714} {/eq}

This is very close to {eq}\sqrt{2} \approx 1.414213562 {/eq}

Folding an A4 paper in half means halving its width while maintaining its height. Therefore, the aspect ratio of each half is

{eq}\dfrac{\frac{297}{2} \text{ mm}}{210 \text{ mm}} = \dfrac{99}{140} \approx \boxed{0.7071428571} {/eq}


Learn more about this topic:

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What is Ratio in Math? - Definition & Overview

from CAHSEE Math Exam: Help and Review

Chapter 10 / Lesson 14
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