To find the length of segment UW, we can use the fact that U is the midpoint of segment RS and W is the midpoint of segment TR. Since RST is an equilateral triangle, segment RS has the same length as segment RT.
Since the length of segment TR is given as 15.9, the length of segment RS is also 15.9.
Segment UW is the sum of segments UR and RW. Given that segment UR has a length of 12 and segment RW has a length of 15.9/2 = 7.95, we can add these lengths together to find the length of segment UW.
UW = UR + RW = 12 + 7.95 = 19.95
Therefore, the length of segment UW is 19.95.
The correct answer is: 19.95