Q. 184.1( 25 Votes )

# Seg AM is a median of ∆ ABC. If AB = 22, AC = 34, BC = 24, find AM

Answer :

We know, By Apollonius theorem

In ΔABC**,** if M is the midpoint of side BC, then AB^{2} + AC^{2} = 2AM^{2} + 2BM ^{2}

Given that,

AB = 22, AC = 34, BC = 24

AP is median i.e. P is the mid-point of BC

Putting values in equation

⇒ 22^{2} + 34^{2} = 2AM^{2} + 2(12)^{2}

⇒ 484 + 1156 = 2AM^{2} + 288

⇒ 1352 = 2AM^{2}

⇒ AM^{2} = 676

⇒ AM = 26

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