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Its not generalised though!!

It's a start...
Let's say we have x^2 + y^2 = z^2 and xy = 2n^2 (triangle area)

Okay so we take it as hypothesis and prove it a contradiction..I'll try

|dw:1350135906515:dw|

|dw:1350136054246:dw|

Promising...how will you get a quartic so as to use the given?

You need to multiply the first line of your first post with something...

Writing your first line in full:
(x+y)^2 = x^2 + y^2 +2xy = z^2 + 4n^2

|dw:1350136543480:dw|

(x+y)^2 = x^2 + y^2 +2xy = z^2 + 4n^2 Your first line
(x-y)^2 = x^2 + y^2 -2xy = z^2 -4n^2

oh!!

:-)

that would yield extra non dependent solution.

*equation (solution)

We, are just trying to get a contradiction....

We are assuming a triangle that is square....

yeah ... three variables 3 non dependent equations ... it's possible to deduce from that.

yeah i see the trick!!

U almost had it, a bit more time, u would have had it, I think....

well .. I'm not too good with algebraic manipulations.

I shall put up a few more while it's stil quiet....

I usually takes quite lot more than necessary steps to do things.