Hello, GAdams!

When you cut a piece of A4 paper in half (portrait, cut across)

you get two pieces of A5 paper.

A5 paper is similar to A4 paper.

Express the length of A5 paper as a percentage of the length of A4 paper.

Another approach (to me, the obvious one) . . . make a sketch! Code:

- *-----------* -
: | | :
: | | ½L
: | | :
L * - - - - - * -
: | | :
: | | ½L
: | | :
- *-----------* -
: W :

A4 has length $\displaystyle L$, width $\displaystyle W$.

A5 has length $\displaystyle W$, width $\displaystyle \frac{1}{2}L$.

We want the ratio: .$\displaystyle \frac{W}{L}$

Since the rectangles are similar: .$\displaystyle \frac{W}{\frac{1}{2}L} \:=\:\frac{L}{W}\quad\Rightarrow\quad W^2\:=\:\frac{1}{2}L^2\quad\Rightarrow\quad\frac{W ^2}{L^2} \:=\:\frac{1}{2}

$

Hence: .$\displaystyle \left(\frac{W}{L}\right)^2 \:=\:\frac{1}{2}\quad\Rightarrow\quad \frac{W}{L} \:=\:\frac{1}{\sqrt{2}} \:=\:0.707106781 $

Therefore: $\displaystyle W$ is about **70.7%** of $\displaystyle L$.