The two traingles, VSU and TSR are similar by SAS similarity criteria.
According to the diagram,
UT = TS
and
VR = SR
[tex] \frac{ST}{SU} = \frac{ST}{ST + SU} \\ = \frac{ST}{2ST} = \frac{1}{2} [/tex]
Similarly for all sides the ratio must be same.
Applying this on the side required here,
[tex] \frac{RT}{VU} = \frac{1}{2} \\ \\ \frac{p - 6}{p} = \frac{1}{2} \\ 2p - 12 = p \\ p = 12[/tex]
Therefore p = 12 units= UV .
