---      ---
\  \    /  /
 \  \  /  /
  \  \/  /
   \    /
    \  /
     \/

A nice letter V is crudely shown above.
The goal is to get its center of gravity to be at the exact point where the two inner diagonal segments meet.

Case 1: Find the width of the V if the two horizontal segments are one unit long and the overall height of the V is three units.

Case 2: The width and the height are each one unit. Find the lengths of the horizontal segments.