Answer:
PQ measures 36 units.
Step-by-step explanation:
Line RS bisects segment PQ at R. By the definition of a bisector:
[tex]\displaystyle PR = RQ[/tex]
Hence:
We are given that RQ = x + 9 and RP = 2x, and we want to determine PQ.
Solve for x. Substitute:
[tex]\displaystyle (2x) = (x+9)[/tex]
Hence:
[tex]\displaystyle x = 9[/tex]
PQ is given by:
[tex]\displaystyle PQ = PR + RQ[/tex]
Since PR = RQ:
[tex]\displaystyle PQ =2PR[/tex]
Substitute and evaluate:
[tex]\displaystyle \begin{aligned} PQ &= 2PR \\ &= 2(2x) \\ &= 4x \\ &= 4(9) \\ &= 36 \end{aligned}[/tex]
Hence, PQ measures 36 units.
