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## 'Fit for Photocopying' printed from http://nrich.maths.org/

This problem builds on the ideas
about length and area scale factors of enlargement introduced
in Growing Rectangles.

You may be familiar with the standard paper size $A4$. Two
sheets of $A4$ fit together to make a sheet of $A3$, two sheets of
$A3$ fit together to make a sheet of $A2$, and so on.

A sheet of $A0$ has an area of $1$ square metre.

Each member of the $A$ paper size
family is an enlargement of the others - they are similar
shapes.
What scale factor of enlargement would you need to scale $A4$ to
$A3$, $A2$, $A1$ and $A0$?

What would happen if you started at $A5$ instead of $A4$?

What would the scale factors be if you scaled from the larger
sheets to the smaller ones?

Can you write down an expression for the scale factor of
enlargement needed to get from $A(n)$ paper to $A(m)$ paper?

(You may wish to consider separately the case where $n > m$ and
where $n < m$).

On a photocopier, approximately what percentage would you need to
scale by in order to photocopy an $A3$ poster onto $A4$
paper?

Here are some challenging
questions to consider:
Can you express the length of the longer side of a sheet of paper
from the $A$ family in terms of its shorter side?

Given that a sheet of $A0$ has an area of $1$ square metre, can you
work out its dimensions?

Can you use this together with your previous results to work out
the exact dimensions of a sheet of $A4$ paper?

Can you find a consistent way to define $A(-1)$ and other negative
paper sizes?

Can you find a consistent way to define $A(\frac{1}{2})$, and other
fractional paper sizes?