The lengths of the segments QS and TV are QS = 8 and TV = 8
How to determine the length of the segments QS and TV
From the question, we have the following parameters that can be used in our computation:
QRS = TUV
Also, we have
QS = 3v+2 and TV = 7v - 6
This means that
3v + 2 = 7v - 6
So, we have
7v - 3v = 2 + 6
4v = 8
Divide both sides by 4
v = 2
Recall that
QS = 3v+2 and TV = 7v - 6
So, we have
QS = 3 * 2 + 2 and TV = 7 * 2 - 6
Evaluate
QS = 8 and TV = 8
Hence, the lengths of the segments QS and TV are QS = 8 and TV = 8