A question in space geometry

[Chen]

Ok, you take a rectangular and fold it along one of its diagonal, so that the two planes are perpendicular to each other.

Using a and b, what is the distance between the points A and B (d)?

My anwer is:
d = \sqrt{a^2 + b^2 - \frac{2a^2b^2}{a^2 + b^2}} = \sqrt{\frac{a^4 + b^4}{a^2 + b^2}}
But I doubt that it's actually correct. :)

[Chen]

By the way, this is how I solved it (see attachment). I found x and f with Pythagoras, and using f I found y with the cosine law (the extended Pythagoras thing [;)]). And from there I just used x and y to find d with Pythagoras.

So is this correct, and is there an easier way to do this?

[verty]

I got the same answer so I am sure it is correct. The only slight difference in what I did was I used the two perpendicular heights and the distance between them.