Maths-
General
Easy

Question

△ PQR is a right triangle with ∠Q=90 M is the midpoint of QR. Prove that

The correct answer is: Hence proved


    P M squared equals P R squared minus 3 Q M squared


    As M is mid point of QR then, QM = ½ RQ
    We get PR squared equals PQ squared plus left parenthesis 2 QM right parenthesis squared not stretchy rightwards double arrow PR squared equals PQ squared plus 4 Q straight Q squared —Eq1
    Applying Pythagoras theorem For triangle PQM
    PM squared equals PQ squared plus QM squared —Eq2
    Substitute Eq2 in Eq1
    We get
    PR squared equals PQ squared plus QM squared plus 3 Q straight Q squared
    not stretchy rightwards double arrow PR squared equals PM squared plus 3 QM squared not stretchy rightwards double arrow PM squared equals PR squared minus 3 QM squared
    Hence proved

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