A net enclosure for practicing golf shots is open at one end as shown below $($shaded region$).$ The end is a square and netting is used for the sides, top, and one end. Find the dimensions that minimize the amount of netting required and give a volume of $144m^3.$ Round your answer to $1$ decimal place.

$[7]$

${?}^{****}$ Note, the shaded region is NOT the bottom of the enclosure $-$ it is the rightmost side panel as shown.