If there is nothing new about my method then why do you not see "c^2 = cx + cy" in the text books? Or anything pertaining to c = x + y? Exactly! Because it is new. 5 * (1.8+3.2) = 5^2. So the sqrt of 5x = one side of the triangle. This is completely new.There is nothing new to your method. All you do is to choose the length of the hypotenuse (here: 5) plus one additional length in your triangle (here: 1.8). You use Pythagoras in an implicit way, as pwsnafu showed. You find three values c,a,b which satisfy c^2=a^2+b^2 by construction.
In the same way, you could directly choose another side length:
5 and 2 give sqrt(5^2-2^2)=sqrt(21) as third side.
5 and 3 give sqrt(5^2-3^2)=sqrt(16)=4 as third side.