I think it would be clearer with an explicit function of a rectangle's area with respect to its diagonals: A = x y x = r

I think it would be clearer with an explicit function of a rectangle's area with respect to its diagonals: A = x y x = r cos(θ) y = r sin(θ) => A(r) = r²cos(θ)sin(θ) A(c) = A(a) + A(b) = c²cos(θ)sin(θ) = a²cos(θ)sin(θ) + b²cos(θ)sin(θ) => c² = a² + b²