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Question
In ΔPQR, seg PM is the median. If PM = 9, PQ2 + PR2 = 290, Find QR.
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Solution
PM = 9 ; PQ2 + PR2 = 290
To find QR
∵ PM is the median of QR.
So, by apollonius theorem,
PQ2 + PR2 = 2 PM2 + 2 QM2
290 = 2(9)2 + 2(QM)2
290 = 2 [81 + (QM)2]
145 = 81 + QM2
QM2 = 145 - 81
QM2 = 64
QM = 8
QM = 2 × QM = 2 × 8 = 16 units
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