# Thread: Similar shapes question

1. ## Similar shapes question

I'm stuck on the following question :

An A3 sheet of paper can be cut into 2 sheets of A4.
The A3 and A4 sheets are mathmatically similar.

Find the scale factor: (long side of A3 sheet) ie. x
(long side of A4 sheet) y

I do actually know that the correct answer to this question is the square root of 2 but I need to show how this has been worked out and I don't have a clue.

Thanks
Richie

2. Hello, Richie92!

An A3 sheet of paper can be cut into 2 sheets of A4.
The A3 and A4 sheets are mathmatically similar.

Find the scale factor: .x/y
. . where x = long side of A3, y = long side of A4.

A3 is an x-by-y rectangle.
Code:
                x
* - - - - - - - - - *
|                   |
|                   |
y |        A3         | y
|                   |
|                   |
* - - - - - - - - - *
x

It is bisected into two rectangles where A3 ~ A4.
Code:
          ½x
* - - - - *
|         |
|         |
y |   A4    |y
|         |
|         |
* - - - - *
½x

. . . . . . . . ½x . . . y . . . . .
We have: . ---- .= .-- . . --- .= .2
. . . . . - - - .y . . - .x . . . . .

. . . . - - . . .x . . . . _
Therefore: . -- .= .√2
. . . . - - . . .y