2005 Fermat Problem 20

In triangle ABC, if AB = AC = x + 1 and BC = 2x - 2, where x > 1, then the area of the triangle is always equal to

\textbf{(A)}\ (x - 1)\sqrt{2x^2 + 2}\quad \textbf{(B)}\ 2(x - 1)\quad \textbf{(C)}\ \frac{1}{2}(x + 1)^2\quad \textbf{(D)}\ (x + 1)(x - 1)\quad \textbf{(E)}\ 2(x - 1)\sqrt{x}

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