1.

In ΔPQR, ∠Q=90°, PQ=12, QR=5 and QS is a median. Find L(QS).

Answer»

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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