Answer: The length of segment QV is 44 units.
Step-by-step explanation:
Consider Δ STR and ΔQTR,
∠TRQ = ∠TRS = 90°
TR = TR (Common)
SR = RQ (Given)
So, ΔTSR ≅ ΔTQR ( By SAS Congruence Criterion)
So, By CPCT (Correspondence part of congruent triangle)
TS = TQ
[tex]2x+8=40\\\\2x=40-8\\\\2x=32\\\\x=\frac{32}{2}\\\\x=16[/tex]
similarly, ΔSVR ≅ ΔQVR
so, SV = QV
[tex]QV=3x-4=3\times 16-4=48-4=44\ units[/tex]
Hence, the length of segment QV is 44 units.
