Question

All help is much appreciated I really need it please

Answer 1

The two traingles, VSU and TSR are similar by SAS similarity criteria.

According to the diagram,
UT = TS
and
VR = SR


$\frac{ST}{SU} = \frac{ST}{ST + SU} \\ = \frac{ST}{2ST} = \frac{1}{2}$

Similarly for all sides the ratio must be same.
Applying this on the side required here,

$\frac{RT}{VU} = \frac{1}{2} \\ \\ \frac{p - 6}{p} = \frac{1}{2} \\ 2p - 12 = p \\ p = 12$


Therefore p = 12 units= UV .