Answer
The length of QV is 31 units
Explanation
Notice that triangle STR and triangle TQR are congruent by Side-Angle-Side, so ST = TQ
We also know that TQ = 26, and we can infer from our diagram that [tex]ST = 3x+2[/tex], so let's replace the values:
ST = TQ
[tex]3x+2=26[/tex]
[tex]3x=24[/tex]
[tex]x=\frac{24}{3}[/tex]
[tex]x=8[/tex]
Also, notice that triangle SVR is congruent to Triangle VQR by Side-Angle-Side as well, so QV = SV
We know that [tex]SV=4x-1[/tex], so let's replace the value:
[tex]QV=4x-1[/tex]
Since we know that [tex]x=8[/tex], we can replace the value to find QV:
[tex]QV=4x-1[/tex]
[tex]QV=4(8)-1[/tex]
[tex]QV=32-1[/tex]
[tex]QV=31[/tex]
