Question

Show that area of Pythagorean triangle x,y,z cannot be square

(U can use that a^4-b^4 = c^2 has no positive solution)

Answer 1

the base and height of pythagorean triangle are 3d and 4d where d is a constant
Area = 1/2 x 3d x 4d = 3d x 2d = 6d^2 this is never a square

Answer 2

Its not generalised though!!

Answer 3

It's a start...

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

Answer 4

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