>>> You're baffled as to why two different rectangles with different side 
>>> lengths but equivalent diagonals have different areas?
> 
>> Yes. I was under the impression that the square of the diagonal was 
>> equal to the sum of the squares of the sides, which _should_ mean that 
>> as one side gets shorter, the other side gets longer by exactly the same 
>> amount, holding the area constant.
> 
>   That would mean that if one of the sides had zero length, then the other
> side would have the same length of the diagonal and the area would still
> be the same. Which is obviously impossible.
> 
>   You are confusing the sum of the squares of the side lengths with the
> product of the side lengths. Obviously they are different things.

Yes. Obviously I am wrong, since the actual results do not match my 
expectations. All I said was that I am surprised. ;-)

Ironically, I'm currently reading

http://www.apa.org/journals/features/psp7761121.pdf

I guess I'm too stupid to realise how stupid I am... :-/

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