Question

In an equilateral angle PQR, the point S the midpoint of QR. angle PSQ=90°.
To prove 4PS² = 3QR²​

Answer 1

Given info : In an equilateral triangle PQR, the point S is the midpoint of QR and angle PSQ = 90°

To prove : 4PS² = 3QR²

solution : as S is the midpoint of QR, QS = (QR)/2 ...(1)

∆PQR is an equilateral triangle.

so, PQ = QR = PR ...(2)

∵ ∠PSQ = 90°

so ∆PQS is a right angled triangle.

where PQ = hypotenuse , PS = altitude and QS = base

from Pythagoras theorem,

hypotenuse² = altitude² + base²

⇒PQ² = PS² + QS²

⇒QR² = PS² + (QR/2)² [ from eq (1) and (2) ]

⇒QR² = PS² + QR²/4

⇒4QR² - QR² = 4PS²

⇒3QR² = 4PS²

hence proved.

Answer 2

Answer:

this is the answer

best of luck