GMAT Quantitative Reasoning Practice Test 2

Normalize each dimension to the width of the cube $\left(\mathit{W}\right)$.
The length is 3 times the width, therefore its $3\mathit{W}$, which is half of the height $\left(6\mathit{W}\right)$.
The volume of the cube is $13,122=6\mathit{W}\times 3\mathit{W}\times \mathit{W}=18{\mathit{W}}^{\mathit{\beta }}{\mathit{W}}^{\mathit{\beta }}=729,\mathit{W}=9$.
The height of the cube is six times the width, therefore its 54 meters.