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Triangle Perimeter and Semi-Perimeter (Posted on 2015-01-04) Difficulty: 3 of 5
Consider a triangle ABC each of whose sides and area is an integer.

Prove separately each of these assertions:

(i) Perimeter of triangle ABC is always even.
(ii) Semi-perimeter of triangle ABC is always composite.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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Some Thoughts Extending the theorem Comment 3 of 3 |
I think that my part 2 proof can be extended to prove that if the sides are integral and the area is rational, then either:

a) The perimeter is odd and composite
b) The perimeter is even and the semi-perimeter is composite

  Posted by Steve Herman on 2015-01-04 19:20:58
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