Question

in an equilateral triangle pqr seg ps perpendicular to the side qr. prove that ps square =3qs square​

Answer 1

Given : in an equilateral triangle pqr seg ps perpendicular to the side qr.

To Find : prove that ps² =3qs²

Solution:

equilateral triangle pqr

=> PQ = QR = PR

PS ⊥ QR

ΔPQS and Δ PRS

PQ = PR

PS = PS common

∠PSQ = ∠PSR = 90°

ΔPQS ≅  Δ PRS  ( RHS)

=>  QS = RS

=> QS = QR/2

=> QR = 2QS

=> PQ = 2QS

in  ΔPQS

PS² + QS²  = PQ²

=> PS²  + QS²  = (2QS)²

=> PS²  + QS²  =4QS²

=> PS²    = 3QS ²

QED

Hence Proved

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