Chapter: Pythagoras Theorem· Mathematics Part 2 (Geometry)
Answer: QR = 12
S is the midpoint of QR, so seg PS is a median of \(\Delta PQR\).
By Apollonius theorem, \(PQ^2 + PR^2 = 2PS^2 + 2QS^2\).
\(11^2 + 17^2 = 2 \times 13^2 + 2QS^2\) \(\therefore 121 + 289 = 338 + 2QS^2\)
\(\therefore 410 - 338 = 2QS^2\) \(\therefore 2QS^2 = 72\) \(\therefore QS^2 = 36\) \(\therefore QS = 6\).
\(QR = 2 \times QS = 12\).