SOLUTION: How many distinct triangles with positive integer side lengths have perimeter equal to 50? (1) 48 (2) 50 (3) 51 (4) 49 (5) None of the above

Question 276010: How many distinct triangles with positive integer side lengths have perimeter equal to 50?
(1) 48 (2) 50 (3) 51 (4) 49 (5) None of the above
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
How many distinct triangles with positive integer side lengths have perimeter equal to 50?
(1) 48 (2) 50 (3) 51 (4) 49 (5) None of the above
triangles have 3 sides A, B, C
B-C < A < B+C
A-C < B < A+C
A-B < C < A+B
0 A B C sum
1 2 24 24 50
2 3 23 24 50
3 4 22 24 50
4 4 23 23 50
5 5 21 24 50
6 5 22 23 50
7 6 20 24 50
8 6 21 23 50
9 6 22 22 50
10 7 19 24 50
11 7 20 23 50
12 7 21 22 50
13 8 18 24 50
14 8 19 23 50
15 8 20 22 50
16 8 21 21 50
17 9 17 24 50
18 9 18 23 50
19 9 19 22 50
20 9 20 21 50
21 10 16 24 50
22 10 17 23 50
23 10 18 22 50
24 10 19 21 50
25 10 20 20 50
26 11 15 24 50
27 11 16 23 50
28 11 17 22 50
29 11 18 21 50
30 11 19 20 50
31 12 14 24 50
32 12 15 23 50
33 12 16 22 50
34 12 17 21 50
35 12 18 20 50
36 12 19 19 50
37 13 13 24 50
38 13 14 23 50
39 13 15 22 50
40 13 16 21 50
41 13 17 20 50
42 13 18 19 50
43 14 14 22 50
44 14 15 21 50
45 14 16 20 50
46 14 17 19 50
47 14 18 18 50
48 15 15 20 50
49 15 16 19 50
50 15 17 18 50
51 16 16 18 50
52 16 17 17 50
unless I did a mistake I count 52, so none of the above

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