In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is \(17\). What is the greatest possible perimeter of the triangle?

This note is part of the set Pre-RMO 2014

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TopNewestApplying triangle inequality we get that the only possible values of a side are 5,6,7,8 of which the side 8 will give maximum perimeter. Hence 8+24+17=49

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49

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49

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\(\color{red}{\boxed{49}}\)

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49

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a first side is 8 then the 2nd side 24, then 17 is a length of a third side add all possible sides the result is 49

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8+24+17=49

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49

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