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

Question

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

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Luna 4 weeks 2021-11-03T19:37:24+00:00 1 Answer 0 views 0

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    2021-11-03T19:39:05+00:00

    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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