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Dutch Mathematical Olympiad

Geometry Difficulty 4.8 AIME Find the answer Netherlands

In the left square, rectangle $ABFE$ is drawn. In the right square, rectangle $PSRQ$ is drawn, where the sides $QR$ and $PS$ are parallel to the diagonal $AC$ of the square. The sides of both squares have length $6$ . It turns out that the rectangles $ABFE$ and $PSRQ$ have exactly the same dimensions.

What is the length of $AE$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

$6\sqrt{2} - 6$

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