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प्रश्न
In ΔPQR, seg PM is a median, PM = 9 and PQ2 + PR2 = 290. Find the length of QR.
Seg PM is a median of ΔPQR, PM = 9 and PQ2 + PR2 = 290, then find QR.
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उत्तर
Given: PM = 9,
PQ2 + PR2 = 290
To find QR
∵ PM is the median of QR.
QM = MR ...(i)
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 = MR = 8 units ...[From (i)]
QR = QM + MR ...[∵ QNR is a straight line]
QR = 8 + 8
QR = 16 units.
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