In ∆ABC, seg AM is the median. [Given]
∴ M is the midpoint of side BC.
∴ MC = 1/2 BC
= 1/2 × 24 = 12 units
Now, AB2 + AC2 = 2 AM2 + 2MC2 [Apollonius theorem]
∴ 222 + 342 = 2AM2 + 2 (12)2
∴ 484 + 1156 = 2 AM2 + 2 (144)
∴ 1640 = 2AM2 + 2 (144)
∴ 820 = AM2 + 144 [Dividing both sides by 2]
∴ AM2 = 820 – 144
∴ AM2 = 676
∴ AM = √676 [Taking square root of both sides]
∴ AM = 26 units
