Given that U is the midpoint of QT and S is the midpoint of RT, let's first define our line segments:
- QR is the full length of the line segment from Q to R.
- Since U is the midpoint of QT, QU is half of QT.
- Since S is the midpoint of RT, RS is half of RT.
With QR being 54, we can establish the following:
1. Since S is the midpoint of RT, RS is half of QR, which means RS = QR / 2. So, RS = 54 / 2 = 27.
2. However, SU is a segment that starts from the midpoint of RT (which is S) and goes to U. To find SU, we first need to determine the length of RU, which is the second half of QR.
We know the full length of QR is 54, and RS is 27, so RU, which is the remaining part from R to U, must also be 27, since S is at the midpoint.
3. Since SU is a part of RU and S is the midpoint, SU is half of RU. Therefore, SU is half of 27.
So, SU = RU / 2 = 27 / 2 = 13.5
The length of SU is 13.5.
