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Pre-RMO 2014/4

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

Note by Pranshu Gaba
2 years, 9 months ago

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Applying 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 · 2 years, 9 months ago

49 · 1 year, 9 months ago

49 · 1 year, 11 months ago

$$\color{red}{\boxed{49}}$$ · 1 year, 11 months ago

49 · 2 years, 2 months ago

49 · 2 years, 8 months ago

49 · 2 years, 9 months ago

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 · 2 years, 9 months ago

49 · 2 years, 9 months ago

8+24+17=49 · 2 years, 9 months ago