segment pm is a median of triangle pqr if PQ is equals to 40 PR is equal to 42 and pm is equal to 29 find QR
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Answered by
1
Answer:
Seg PM is a median of ΔPQR. If PQ=40,PR=42 and PM=29,
then QR = 58
Let draw an perpendicular from P at QR at point D
Then
PR² = PD² + RD²
PR² = PD² + (RM + MD)²
PQ² = PD² + QD²
=> PQ² = PD² + (QM - MD)²
Adding both
PR² + PQ² = PD² + (RM + MD)² + PD² + (QM - MD)²
=> PR² + PQ² = PD² + RM² + MD² +2RM.MD + PD² + QM² + MD² - 2QM.MD
as RM = QM (PM is median)
=> PR² + PQ² = PD² + RM² + MD² + PD² + RM² + MD²
=> PR² + PQ² = 2(PD² + MD²) + 2RM²
PD² + MD² = PM²
=> PR² + PQ² = 2PM² + 2RM²
PQ = 40
PR = 42
PM = 29
=> 42² + 40² = 2 * 29² + 2RM²
=> 1764 + 1600 = 1682 + 2RM²
=> 2RM² = 1682
=> RM² = 841
=> RM = 29
QR = RM + QM
=> QR = 29 + 29 = 58
QR = 58
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Answered by
3
Answer:
In PQR, PM is medium
By apollonius theorem
QR=58 cm.
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