Question

In ∆ABC, Seg AP
is a medium ,BC = 18 units,
AB²+ AC² 260 Find AP.
2​

Answer 1

Answer:

Given :

In ∆ ABC , AP is a median , BC = 18 & AB² + AC² = 260

In ∆ ABC , seg AP is a median. P is the midpoint of seg BC

BP = PC = 1/2BC

BP = PC = ½(18) = 9

AB² + AC² = 2AP² + 2PC²

[ By APOLLONIUS THEOREM, this theorem tells us the relation among the sides and medians of a triangle.]

AB² + AC² = 2(AP² + PC²)

260 = 2(AP² + 9²)

260/2 = AP² + 81

130 = AP² +81

130 - 81 = AP²

49 = AP²

AP = √ 49 = 7

AP = 7

Hence, the value of AP is 7 .

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