P
(i) APQR is an equilateral triangle.
seg PS 1 side QR such that Q-S-R.
Prove PSP = 3QS2 by completing the
fo

1 thought on “P<br />(i) APQR is an equilateral triangle.<br />seg PS 1 side QR such that Q-S-R.<br />Prove PSP = 3QS2 by completing the<br />fo”

1. Answer:

   Let the side length of an equilateral triangle ∆PQR is a and PT be the altitude of ∆PQR as shown in figure.

   Now, PQ = QR = PR = a

   We know, in case of equilateral triangle, altitude divide the base in two equal parts. e.g., QT = TR = QR/2 = a/2

   Given, QS = QR/3 = a/3

   ∴ ST = QT – QS = a/2 – a/3 = a/6

   Also PT = √(PQ² – QT²) = √(a² -a²/4) = √3a/2

   Now, use Pythagoras theorem for ∆PST

   PS² = ST² + PT²

   ⇒PS² = (a/6)² + (√3a/2)² = a²/36 + 3a²/4

   = (a² + 27a²)/36 = 28a²/36 = 7a²/9

   ⇒9PS² = 7PQ²

   Hence proved

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