Problem 28

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Problem 28: (2014 AMC 12b, 21)

In the figure, $ABCD$ is a square of side length $1$. The rectangles $JKHG$ and $EBCF$ are congruent. What is $BE$?

$\textbf{(A) }\frac{1}{2}(\sqrt{6}-2)\qquad$ $\textbf{(B) }\frac{1}{4}\qquad$ $\textbf{(C) }2-\sqrt{3}\qquad$ $\textbf{(D) }\frac{\sqrt{3}}{6}\qquad$ $\textbf{(E) } 1-\frac{\sqrt{2}}{2}$

Solution

Exercise 28: Solution

In the figure, $ABCD$ is a rectangle with $AB=4$ and $BC=3$. The rectangles $JKHG$ and $EBCF$ are congruent. What is $BE$?

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