SOLUTION: All the sides of a triangle have integer length. The perimeter of the triangle is 10, and the triangle is scalene. How many such non-congruent triangles are there?

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Question 1210542: All the sides of a triangle have integer length. The perimeter of the triangle is 10, and the triangle is scalene. How many such non-congruent triangles are there?
Answer by greenestamps(13305) About Me  (Show Source):
You can put this solution on YOUR website!


There are no such triangles.

Here is a list of all the combinations of three positive integers with a sum of 10:
1, 1, 8   does not make a triangle
1, 2, 7   does not make a triangle
1, 3, 6   does not make a triangle
1, 4, 5   does not make a triangle

2, 2, 6   does not make a triangle
2, 3, 5   does not make a triangle
2, 4, 4   the triangle is not scalene

3, 3, 4   the triangle is not scalene

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