# 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
6 years ago

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49

- 5 years ago

49

- 5 years, 2 months ago

$\color{#D61F06}{\boxed{49}}$

- 5 years, 2 months ago

49

- 5 years, 5 months ago

49

- 5 years, 11 months ago

49

- 5 years, 12 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

49

- 6 years ago

8+24+17=49

- 6 years ago

49

- 6 years ago

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

- 6 years ago