$3+$ [Properties and characteristics of an isosceles triangle.]

On each side of a square, one point was taken. It turned out that these points are the vertices of a rectangle, the sides of which are parallel to the diagonals of the square. Find the perimeter of the rectangle if the diagonal of the square is 6.

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Let the vertices $K, L, M$ and $N$ of the rectangle $K L M N$ be located on the sides $A B, B C, C D$ and $A D$ of the square $A B C D$, respectively, such that $K N \| B D$ and

$K L \| A C$, and the segments $K L$ and $M N$ intersect the diagonal $B D$ of the square at points $P$ and $Q$, respectively. Then $K P=B P$, $N Q=D Q, K N=P Q$.

## Answer

12.