Question 239613: How many scalene triangles have a perimeter of less than 13?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
The way you ask the question, an infinite number. However, if you restrict the measures of the sides to the integers, then there is a small finite set of three integer sets such that no set of three has a duplicated integer and the sum of each set is 13.
For example, 1, 2, and 10 is one such set
1, 3, 9
and so on. Then
2, 3, 8
2, 4, ...
You get the idea. Just be careful not to duplicate any numbers in a set of 3 because if you duplicate, then you no longer have a scalene triangle, you have an isosceles triangle. For example, 3, 5, 5 -- no good.
John
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