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3) In AABC seg AP is a median. If BC 18 and AB +AC 260, find AP. |
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Answer» In ∆ ABC , AP is a median , BC = 18 & AB² + AC² = 260In ∆ ABC , seg AP is a median. P is the midpoint of seg BCBP = PC = 1/2BCBP = 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 + 81130 = AP² +81130 - 81 = AP²49 = AP²AP = √ 49 = 7 AP = 7 Hence, the value of AP is 7 Like my answer if you find it useful! |
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