Answer
a) No
b) TU and UV are 35 units long. TV is 70 units long.
Work Step by Step
a) Because $\overline{PQ}$ and $\overline{QR}$ are congruent, the length of $\overline{QR}$ can be determined by finding the length of $\overline{PQ}$.
b)
$TU=UV\longrightarrow$ definition of midpoint
$8x+11=12x-1\longrightarrow$ substitute
$8x+11-8x=12x-1-8x\longrightarrow$ subtrat 8x from each side
$11=4x-1\longrightarrow$ combine like terms
$11+1=4x-1+1\longrightarrow$ add 1 to each side
$12=4x\longrightarrow$ simplify
$12\div4=4x\div4\longrightarrow$ divide each side by 4
$3=x$
Substitute to find TU and UV.
$TU=8x+11=8(3)+11=24+11=35$
$UV=12x-1=12(3)-1=36-1=35$
Use the segment addition postulate.
$TV=TU+UV=35+35=70.$
