Question 1148034: How many scalene triangles have perimeter less than 16 and sides of integral length?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
(1) If the side lengths are all different integers, then there are no such triangles with the shortest side 1.
(2) If the shortest side is 2 and the lengths are all different integers, then the lengths of the other two sides must differ by only 1.
(2,3,4); (2,4,5); (2,5,6); (2,6,7) 4 triangles
(3) If the shortest side is 3 and the lengths are all different integers, then the lengths of the other two sides can differ by either 1 or 2.
(3,4,5); (3,5,6); (3,4,6); (3,5,7) 4 more triangles
(4) If the shortest side is 4 and the lengths are all different integers, and the sum of the three lengths is less than 16, then there is only one solution.
(4,5,6) 1 triangle
ANSWER: 4+4+1 = 9 such triangles
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