Question
Determine which set of side measurements could be used to form a triangle.
12, 23, 7
10, 7, 2
8, 3, 11
5, 11, 8
12, 23, 7
10, 7, 2
8, 3, 11
5, 11, 8
Answers
Answered by
GPT 3.5
In order for a triangle to be formed, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check each set of side measurements:
1) 12, 23, 7
12 + 23 = 35 > 7 and 12 + 7 = 19 > 23, but 23 + 7 = 30 < 12, so this set of side measurements cannot form a triangle.
2) 10, 7, 2
10 + 7 = 17 > 2, but 10 + 2 = 12 < 7, and 7 + 2 = 9 < 10, so this set of side measurements cannot form a triangle.
3) 8, 3, 11
8 + 3 = 11 > 11, 8 + 11 = 19 > 3, and 3 + 11 = 14 > 8, so this set of side measurements can form a triangle.
4) 5, 11, 8
5 + 11 = 16 > 8, 5 + 8 = 13 > 11, and 11 + 8 = 19 > 5, so this set of side measurements can form a triangle.
Therefore, the sets of side measurements that could be used to form a triangle are 8, 3, 11 and 5, 11, 8.
Let's check each set of side measurements:
1) 12, 23, 7
12 + 23 = 35 > 7 and 12 + 7 = 19 > 23, but 23 + 7 = 30 < 12, so this set of side measurements cannot form a triangle.
2) 10, 7, 2
10 + 7 = 17 > 2, but 10 + 2 = 12 < 7, and 7 + 2 = 9 < 10, so this set of side measurements cannot form a triangle.
3) 8, 3, 11
8 + 3 = 11 > 11, 8 + 11 = 19 > 3, and 3 + 11 = 14 > 8, so this set of side measurements can form a triangle.
4) 5, 11, 8
5 + 11 = 16 > 8, 5 + 8 = 13 > 11, and 11 + 8 = 19 > 5, so this set of side measurements can form a triangle.
Therefore, the sets of side measurements that could be used to form a triangle are 8, 3, 11 and 5, 11, 8.