Question

In equaliteral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes ?

Answer 1

Step-by-step explanation:

I hope this will help....

Answer 2

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It is given that :-

TRIANGLE (PQR) in which PQ = QR = RP also PN is perpendicular to QR

Now,

To Prove

3PQ² = 4AN²

Proof :-

In Triangle PNQ also in triangle PNR

PQ = PR (Given)

∠Q = ∠R = 60°

Therefore,

∆PNQ is congruent to ∆PNR (By SAA rule)

Therefore,

QN = NR =½QR

Now,

From right ∆PNQ

PQ² = PN² + QN² (Pythagoras theorem)

⇒ PN² + (½QR)²

⇒ PN² + ¼QR²

⇒ 4PQ² = 4PN² + QR²

⇒ 3PQ² = 4PN² (QR = PQ)

Therefore we get ,

3PQ² = 4PN²