Form an equation involving x and y?

Question

A lot of paper comes in standard sizes A0; A1; A2; A3 etc. A0 can be cut in half to give two sheets of A1; A1 can be cut in half to give two sheets of A2 and so on.

Call the sides of A1 x and y (y being the longest edge)

1. All the pieces of paper are similar. Form an equation involving x and y that shows this.

No more details were given. Any help appreciated.

Answer 1

This says that they are in the same proportion as you cut them in half,

in other words the ration of length to widths are equal.

A1 is x by y, so A2 is y/2 by x

x/y = y/(2x)

y^2 = 2x^2

y/x = sqrt(2)

or

y = x * sqrt(2)

Answer 2

too many numbers lets skip the maths

Answer 3

A0=y

A1=x

A1=A0/2

x=y/2

2x=y

2x-y=0

Answer 4

Christ I need a drink after straying into this category by mistake lol.