Let $$n \geq 1$$ be an integer and consider the sum $$x=\sum_{k \geq 0}^{}\left(_{2k}^{n}\right)2^{n-2k}3^{k}=\left(_{0}^{n}\right)2^{n}+\left(_{2}^{n}\right)2^{n-2}.3+\left(_{4}^{n}\right)2^{n-4}.3^{2}+....$$ Show that $$2x − 1, 2x, 2x + 1$$ form the sides of a triangle whose area and inradius are also integers.