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In ΔPQR, ∠Q=90°, PQ=12, QR=5 and QS is a median. Find L(QS). |
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Answer» L(QS) = 6.5 Step-by-step explanation: In ΔPQR, ∠Q=90°, PQ=12, QR=5 PR² = PQ² + QR² (using Pythagoras THEOREM) => PR² = 12² + 5² => PR² = 169 => PR = 13 QS is median => PS = RS = 13/2 = 6.5 cm in ΔPQR Cos ∠P = PQ/PR = 12 /13 in Δ PQS QS² = PQ² + PS² - 2*PQ*PSCos∠P => QS² = 12² + 6.5² - 2 * 12 * 6.5 * (12/13) => QS² = 12² + 6.5² - 12² => QS² = 6.5² => QS = 6.5 L(QS) = 6.5 |
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