CEMC Fermat, 2005

Geometry Difficulty 3.0 AMC 10/12 Find the answer Canada

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

(A) $(x - 1)\sqrt{2x^2 + 2}$ (B) $2(x - 1)$ (C) $\dfrac{1}{2}(x + 1)^2$ (D) $(x + 1)(x - 1)$ (E) $2(x - 1)\sqrt{x}$

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