The figure above shows a triangular prism whose base is a equilateral triangle with side lengths $x$ and height $\sqrt{3} x$. If the volume of the prism is $\frac{81}{4}$, what is the value of $x$ ?
Choices:
A:3
B:4
C:5
D:6
Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.
Question: The figure above shows a triangular prism whose base is a equilateral triangle with side lengths $x$ and height $\sqrt{3} x$. If the volume of the prism is $\frac{81}{4}$, what is the value of $x$ ?
Choices:
A:3
B:4
C:5
D:6
Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: The figure above shows a triangular prism whose base is a equilateral triangle with side lengths $x$ and height $\sqrt{3} x$. If the volume of the prism is $\frac{81}{4}$, what is the value of $x$ ?
Choices:
A:3
B:4
C:5
D:6