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Answer:
(b) ΔPQR ~ Δ STR, PR = 16, SR = 12
Explanation:
The similar triangles are ...
ΔPQR ~ ΔSTR . . . . by AA similarity: S ≅ P; ∠SRT ≅ ∠PRQ
Corresponding sides are proportional, so we have ...
PR/PQ = SR/ST
(x +1)/8 = (x -3)/6
3(x +1) = 4(x -3) . . . . . . multiply by 24
3x +3 = 4x -12 . . . . . . . eliminate parentheses
15 = x . . . . . . . . . . . . . . add 12-3x
Then the side lengths are ...
PR = x+1 = 15 +1 = 16
SR = x -3 = 15 -3 = 12
The similarity statement and side lengths match the 2nd choice.