Question

*Seg PM is a median of △PQR. If PQ = 40, PR = 42 and QR = 58 then find length of PM.*

1️⃣ 25
2️⃣ 20
3️⃣ 21
4️⃣ 29​

Answer 1

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 + 2MR2

∴ 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 = √841 [Taking square root of both sides]

= 29 units

Now, QR = 2 MR [M is the midpoint of QR]

= 2 × 29

∴ QR = 58 units