Given the Pythagorean Theorem a2 + b2 = c2, I interject that unsurprisingly for any right triangle, the square of the area corresponding to the hypotenuse less the same for that of the longer leg and again for that of the shortest leg, the resultant divided by eight, equals the square of the right triangle area.
Reference prior post: Pythagorean Theorem Generalization as Consequence of Three-Dimensions
(c2)2 – (b2)2 – (a2)2 / 8 = (.5ab)2
c4 – b4 – a4 = (.5ab)2 (8)
√(c4 – b4 – a4) / 2√2 = .5ab
√(c4 – b4 – a4) = ab√2
c=±(2b2 a2+ b4 + a4)(1/4)
c=√(b2 + a2)
