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June 3rd, 2014, 04:32 AM   #1
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sequential

ABC is triangle the sides is sequential series
find it
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June 3rd, 2014, 04:49 AM   #2
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uh... 3:4:5?
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June 3rd, 2014, 06:55 AM   #3
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2 with integer areas:
13-14-15 , area 84
51-52-53, area 1170
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June 3rd, 2014, 06:57 AM   #4
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There are infinite number of such triangles.
Such as, the edges of triangle are $\displaystyle x, \; x+ \alpha , \; a+ 2 \alpha$.

Are lengths of edges integers, what type of sequence is it, and etc.?
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June 3rd, 2014, 08:41 AM   #5
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Let m > 0 be an integer and n = $(2+\sqrt3)^m+(2-\sqrt3)^m.$ Then n is an integer and n-1, n, n+1 are the sides of a triangle with integer area.
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June 3rd, 2014, 02:44 PM   #6
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Any 3 integers will do as long as the sum of any two is greater than the third.
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June 3rd, 2014, 09:35 PM   #7
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Quote:
Originally Posted by mathman View Post
Any 3 integers will do as long as the sum of any two is greater than the third.
I can only assume this question is a sort of Rorschach test to see who sees the problem in what ways.
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June 4th, 2014, 12:27 PM   #8
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Quote:
Originally Posted by CRGreathouse View Post
I can only assume this question is a sort of Rorschach test to see who sees the problem in what ways.
You could be right. I am not a mind reader.
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