In ∆PQR, seg PM is the median. [Given]
∴ M is the midpoint of side QR.
∴ PQ2 + PR2 = 2 PM2 + 2 MR2 [Apollonius theorem]
∴ 402 + 422 = 2 (29)2 + 2 MR2
∴ 1600 + 1764 = 2 (841) + 2 MR2
∴ 3364 = 2 (841) + 2 MR2
∴ 1682 = 841 +MR2 [Dividing both sides by 2]
∴ MR2 = 1682 – 841
∴ MR2 = 841
∴ MR = \(\sqrt{841}\) [Taking square root of both sides]
= 29 units
Now, QR = 2 MR [M is the midpoint of QR]
= 2 × 29
∴ QR = 58 units
