--- --- \ \ / / \ \ / / \ \/ / \ / \ / \/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.