Q18 of 45 Page 43

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


We know, By Apollonius theorem


In ΔABC, if M is the midpoint of side BC, then AB2 + AC2 = 2AM2 + 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


⇒ 222 + 342 = 2AM2 + 2(12)2


⇒ 484 + 1156 = 2AM2 + 288


⇒ 1352 = 2AM2


⇒ AM2 = 676


⇒ AM = 26


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