Puzzle time - area-perimeter match

[jon-nyc]

Find all integer-sided rectangles whose area and perimeter happen to be the same number.

[jon-nyc]

Unless I’m missing something, which is far from impossible, this one was pretty easy.

[Klaus]

Hm, let's see.

:::

It means we want all integer solutions to

a*b = 2a+2b

or

b = 2a / (a-2)

That's a hyperbola, so there can only be finitely many solutions.

I'd say it's these four number pairs.

0,0
3,6
4,4
6,3

:::

(I put this into a defunct spoiler (damn lazy forum admin should fix this); if you want to see what I wrote you can push "Quote")

Yeah, seems to be pretty simple.