If $x, y, z$ are in arithmetic progression with common difference $d, x\ne 3d,$ 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

• Correct answer
  A

  $72$
• B

  $12$
• C

  $36$
• D

  $6$

Hence, the correct answer is option: 'A'.