To determine whether a group of side measures will form a triangle, we need to apply the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's go through each group of side measures:
1. 2, 7, 6
The sum of 2 and 6 is 8, which is greater than 7.
The sum of 2 and 7 is 9, which is greater than 6.
The sum of 6 and 7 is 13, which is greater than 2.
Therefore, the group of side measures 2, 7, and 6 will form a triangle.
2. 9, 4, 3
The sum of 9 and 3 is 12, which is greater than 4.
The sum of 9 and 4 is 13, which is greater than 3.
The sum of 4 and 3 is 7, which is less than 9.
Therefore, the group of side measures 9, 4, and 3 will not form a triangle.
3. 12, 10, 22
The sum of 12 and 10 is 22, which is greater than 22.
The sum of 12 and 22 is 34, which is greater than 10.
The sum of 10 and 22 is 32, which is greater than 12.
Therefore, the group of side measures 12, 10, and 22 will form a triangle.
4. 8, 1, 7
The sum of 8 and 1 is 9, which is less than 7.
The sum of 8 and 7 is 15, which is greater than 1.
The sum of 1 and 7 is 8, which is greater than 8.
Therefore, the group of side measures 8, 1, and 7 will not form a triangle.
So, the groups of side measures that will form a triangle are 2, 7, 6 and 12, 10, 22.
Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle
2, 7, 6
9, 4, 3
12, 10, 22
8, 1, 7
1 answer
1 answer