Apply the triangle inequality theorem and determine which group of side measures will form a triangle
The options are
12,10,22
8,1,7
2,7,6
9,4,3
To apply the triangle inequality theorem, we must determine if the sum of the lengths of any two sides of a triangle is always greater than the length of the remaining side.
Let's check each option:
1) 12, 10, 22:
12 + 10 = 22 (greater than 22). This satisfies the triangle inequality theorem.
10 + 22 = 32 (greater than 12). This satisfies the triangle inequality theorem.
12 + 22 = 34 (greater than 10). This satisfies the triangle inequality theorem.
Therefore, the side measures 12, 10, 22 can form a triangle.
2) 8, 1, 7:
8 + 1 = 9 (less than 7). This does not satisfy the triangle inequality theorem.
1 + 7 = 8 (less than 8). This does not satisfy the triangle inequality theorem.
8 + 7 = 15 (greater than 1). This satisfies the triangle inequality theorem.
Therefore, the side measures 8, 1, 7 cannot form a triangle.
3) 2, 7, 6:
2 + 7 = 9 (greater than 6). This satisfies the triangle inequality theorem.
7 + 6 = 13 (greater than 2). This satisfies the triangle inequality theorem.
2 + 6 = 8 (less than 7). This does not satisfy the triangle inequality theorem.
Therefore, the side measures 2, 7, 6 cannot form a triangle.
4) 9, 4, 3:
9 + 4 = 13 (greater than 3). This satisfies the triangle inequality theorem.
4 + 3 = 7 (greater than 9). This satisfies the triangle inequality theorem.
9 + 3 = 12 (greater than 4). This satisfies the triangle inequality theorem.
Therefore, the side measures 9, 4, 3 can form a triangle.
In summary, the group of side measures that can form a triangle is 12, 10, 22.