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Question
In ΔPQR, ∠Q = 90°, PQ = 12, QR = 5 and QS is a median. Find l(QS).
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Solution
In △PQR, ∠Q = 90° ...[Given]
△PQR is a right angle triangle.
∴ By Pythagoras theorem,
∴ PR2 = PQ2 + QR2
⇒ PR2 = 122 + 52
⇒ PR2 = 144 + 25
⇒ PR2 = 169
⇒ PR = `sqrt169`
⇒ PR = 13
In △PQR,
seg QS is the median on hypotenuse PR.
∴ QS = `1/2`PR ...[In a right angled triangle, the length of the median on the hypotenuse is half the length of the hypotenuse.]
∴ QS = `1/2 × 13`
∴ QS = 6.5 units
Hence, the length of QS is 6.5 units.
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