If $x, y, z$ are in arithmetic progression with common difference $d, x 3 d$, and the determinant of the matrix $\left[\begin{array}{ccc}3 & 4 \sqrt{2} & x \\ 4 & 5 \sqrt{2} & y \\ 5 & k & z\end{array}\right]$ is zero. then the value of $k^2$ is :
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