Q17 of 45 Page 43

Seg PM is a median of ∆ PQR. If PQ = 40, PR = 42 and PM = 29, find QR.


We know, By Apollonius theorem


In ΔPQR, if M is the midpoint of side QR, then PQ2 + PR2 = 2PM2 + 2QM 2


Given that, PM is median i.e. M is the mid-point of QR



And PQ = 40, PR = 42, PM = 29


Putting values,


⇒ (40)2 + (42)2 = 2(29)2 + 2(QM)2


⇒ 1600 + 1764 = 1682 + 2QM2


⇒ QM2 = 1682


⇒ QM = 29


⇒ QR = 2(29) = 58


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