Since RT bisects SU, we can imply that
[tex]\begin{gathered} RT\text{ bisects }SU \\ \Rightarrow SV=VU \\ \text{and} \\ VU=5 \\ \Rightarrow SV=5 \end{gathered}[/tex]
SV=5
Notice that, since SV=VU, triangles VST and VUT are congruent triangles due to the SAS postulate; therefore,
[tex]\begin{gathered} \Delta\text{VST}\cong\Delta VUT \\ \Rightarrow ST\cong UT \\ \Rightarrow ST=23 \end{gathered}[/tex]
ST=23.
Similarly, triangles VSR and VUR are congruent due to the SAS postulate (both share side RV, have a right angle, and SV=UV); thus,
[tex]\begin{gathered} \Delta\text{VSR}\cong\Delta\text{VUR} \\ \Rightarrow SR\cong UR \\ \Rightarrow UR=8 \end{gathered}[/tex]
UR=8
Finally, notice that
[tex]\begin{gathered} SU=SV+VU \\ \Rightarrow SU=2VU\to SV\cong VU \\ \Rightarrow SU=2\cdot5=10 \\ \Rightarrow SU=10 \end{gathered}[/tex]
Thus, SU=10
