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A question states:

The length of each side of a certain triangle is an even number.If no two sides have the same length what is the smallest perimeter the triangle could have ?

According to the author the answer is 18 but i think the answer is 12. (Scalene triangle with 2+4+6 as sides). Any suggestions please?

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I think you are correct. The author takes sides 4,6,8. –  Prasad G Jun 5 '12 at 13:55
Hint: How would a triangle with sides 2, 4 and 6 look like? –  mrf Jun 5 '12 at 13:59
the 2+4+6 figure is not a triangle.. –  Ravi Donepudi Jun 5 '12 at 14:00
The 2+4+6 figure is a "degenerate triangle". Once again, I find three posted answers, and even one "accepted" answer, but no upvotes for the question. (It now has one upvote from me.) –  Michael Hardy Jun 5 '12 at 17:41
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3 Answers

up vote 4 down vote accepted

The sum of the lengths of any two sides of a triangle must be greater than the third side.

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Thanks for the reminder that explains it –  Rajeshwar Jun 5 '12 at 14:08
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Your "triangle" looks like this:

enter image description here

2+4=6, so the long side coincides with the other two.

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The lengths of 2, 4, and 6 as sides imply a trivial triangle with vertices on one line:

remember the triangle inequality $\|x + y\| \le \|x\| + \|y\|$ with equality only if $x,y$ are linearly dependent.

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