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UKMT Intermediate Mathematical Challenge, 2015

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

A rectangle is placed obliquely on top of an identical rectangle, as shown. The area $X$ of the overlapping region (shaded more darkly) is one eighth of the total shaded area. What fraction of the area of one rectangle is $X$ ?

(A) $\frac{1}{3}$ (B) $\frac{2}{7}$ (C) $\frac{1}{4}$ (D) $\frac{2}{9}$ (E) $\frac{1}{5}$

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