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?

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) (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

ANSWER: 0

RELATED QUESTIONS
A scalene triangle has one side 5cm longer than the shortest side and another side 10cm... (answered by josgarithmetic)

What is the smallest possible integer perimeter of a triangle which has sides 5 and... (answered by jim_thompson5910)

How do I find the length of the sides of an acute scalene triangle when I only have the... (answered by stanbon)

the sides of a triangle have lengths 7, 8 and 10. what is the length of the shortest side (answered by jorel1380)

The sides of a triangle have lengths 4,8,and 10. What is the length of the shortest side... (answered by stanbon)

well what is a isosceles triangle and the scalene... (answered by Alan3354)

2 sides of a triangle have lengths 9 and 12. Given that the third side of the triangle... (answered by DrBeeee)

The sides of a triangle have lengths 9,13 and k, where k is an integer. For how many... (answered by fcabanski)

The length of each side of a scalene triangle ABC is a prime number. Find the smallest... (answered by richard1234)