To determine which group of side measures will form a triangle, we can 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 examine each group of side measures:
1) 2, 7, 6:
The sum of the lengths of the two shorter sides is 2 + 6 = 8, which is greater than the length of the longest side (7).
The sum of the lengths of the two longer sides is 2 + 7 = 9, which is greater than the length of the remaining side (6).
Therefore, 2, 7, and 6 can form a triangle.
2) 9, 4, 3:
The sum of the lengths of the two shorter sides is 4 + 3 = 7, which is greater than the length of the longest side (9).
However, the sum of the lengths of the two longer sides is 4 + 9 = 13, which is not greater than the length of the remaining side (3).
Therefore, 9, 4, and 3 cannot form a triangle.
3) 12, 10, 22:
The sum of the lengths of the two shorter sides is 10 + 12 = 22, which is equal to the length of the longest side (22).
Since the sum of the lengths of the two shorter sides is not greater than the length of the longest side, 12, 10, and 22 cannot form a triangle.
4) 8, 1, 7:
The sum of the lengths of the two shorter sides is 1 + 7 = 8, which is equal to the length of the longest side (8).
Since the sum of the lengths of the two shorter sides is not greater than the length of the longest side, 8, 1, and 7 cannot form a triangle.
Therefore, the only group of side measures that can form a triangle is 2, 7, and 6.
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