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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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