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

1.	In ∆PQR, ∠Q = 90°, PQ = 12, QR = 5 and QS is a median. Find l(QS).
Answer» i. PQ = 12, QR = 5 [Given] In APQR, ∠Q = 90° [Given] ∴ PR² = QR² + PQ² [Pythagoras theorem] = 25 + 144 ∴ PR² =169 ∴ PR = 13 units [Taking square root of both sides] ii. In right angled APQR, seg QS is the median on hypotenuse PR. ∴ QS = \(\frac{1}2\)PR [In a right angled triangle, the length of the median on the hypotenuse is half the length of the hypotenuse] = \(\frac{1}2\) x 13 ∴ l(QS) = 6.5 units

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

Answer»

i. PQ = 12, QR = 5 [Given]

In APQR, ∠Q = 90° [Given]

∴ PR² = QR² + PQ² [Pythagoras theorem]

= 25 + 144

∴ PR² =169

∴ PR = 13 units [Taking square root of both sides]

ii. In right angled APQR, seg QS is the median on hypotenuse PR.

∴ QS = \(\frac{1}2\)PR [In a right angled triangle, the length of the median on the hypotenuse is half the length of the hypotenuse]

= \(\frac{1}2\) x 13

∴ l(QS) = 6.5 units