This question has been asked in many other places as well but they're all wrong or unanswered, one of which is: https://web2.0calc.com/questions/plz-help-and-its-not-8-2-whoever-said-that

thanks for any help

By similar trianges, PQ = 3*sqrt(7).

Angles: PQR, PRQ, RTS, and RST are congruent. QR = 8 and SQ = 2. Find PQ.

Hint: QR = QT = 8 Place a point U on PQ so that TU || QR TU = SQ = 2

PQ = 9.237604306