Math Is Fun Forum

Eddie1717

Guest

ratio help!

Hey all, I have a question that I have found two different answers for. Can anyone check my working out and tell me which one is correct. Thanks

The question is to find the value of side x in the rectangle below, the other side being 1. The rectangle is made up of two unit squares and a remaining rectangle that is a scaled down version of the original rectangle.
             
           x
|-----|-----|---|
|       |       |    |   1
|-----|-----|---|

1st way: Combining the two unit squares we know that the side lengths of the small rectangle are (x-2) and 1.

            x
|----------|---|
|              |    |    1
|----------|---|
                x-2

ratio: x/1 = 1/(x-2) we get x= 1+ sqrt(2)

but:
2nd way: Take one unit square away and x becomes (x-1), using the above diagram we get the ratio:

(x-1)/1 = 1/(x-2) and so x= (3 +sqrt(5))/2

I don't know what my error in thinking here is. Can anyone help?

Thanks heaps everyone, this looks like a cool forum!

soroban

Member

Registered: 2007-03-09

Posts: 452

Re: ratio help!

. .

      : - - - -  x  - - - - :
      *-------*-------*-----*
      |       |       |     |
     1|       |       |     |1
      |       |       |     |
      *-------*-------*-----*
      : - 1 - : - 1 - : x-2 :

.