Question

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

Answer 1

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.