M and n are the midpoints of sides QR and PQ respectively of a triangle pqr right angle right angled at Q prove that p m square + r n square = 25 mm square
Answers
Answer:
4(PM² + RN²) = 5PR²
Step-by-step explanation:
data given is not complete
let assume , we have to To Prove
4 (p m square + r n square) = 5 pr²
Given :
M and n are the midpoints of sides QR and PQ respectively
PM² = PQ² + QM²
=> PM² = PQ² + (QR/2)²
=> PM² = PQ² + QR²/4
=> 4PM² = 4PQ² + QR²
Similarly
RN² = QR² + QN²
=> RN² = QR² + (PQ/2)²
=> 4RN² = 4QR² + PQ²
Adding both
4PM² + 4RN² = 4PQ² + QR² + 4QR² + PQ²
=> 4(PM² + RN²) = 5(PQ² + QR²)
=> 4(PM² + RN²) = 5PR²
Answer:
Step-by-step explanation:
4(PM² + RN²) = 5PR²
Step-by-step explanation:
data given is not complete
let assume , we have to To Prove
4 (p m square + r n square) = 5 pr²
Given :
M and n are the midpoints of sides QR and PQ respectively
PM² = PQ² + QM²
=> PM² = PQ² + (QR/2)²
=> PM² = PQ² + QR²/4
=> 4PM² = 4PQ² + QR²
Similarly
RN² = QR² + QN²
=> RN² = QR² + (PQ/2)²
=> 4RN² = 4QR² + PQ²
Adding both
4PM² + 4RN² = 4PQ² + QR² + 4QR² + PQ²
=> 4(PM² + RN²) = 5(PQ² + QR²)
=> 4(PM² + RN²) = 5PR²