Question

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

Answer 1

Step-by-step explanation:

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 = (1/2) PR [In a right angled triangle, the length of the median on the hypotenuse is half the length of the hypotenuse] = (1/2) x 13 ∴ l(QS) = 6.5 units.

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