A trough in the shape of the figure to the right is being filled with water. The shape of the trough is an equilateral triangle prism. The length of the trough is twelve feet.  

1. Find the height of the equilateral triangle in terms of $x$.

   Hint (a):

   Draw and label the triangle with information you know. Use the Pythagorean Theorem to solve for the height.

   Answer (a):

   $\frac{\sqrt{3}}{2}x$

   

2. Find the volume $V$ of the trough in terms of $x$.

   Hint (b):

   $V(x)=$ (area of the triangle)(length of the trough)

3. If the trough can hold $200$ cubic feet of water, how deep is the trough?

   Hint (c):

   Solve $200=V(x)$.