To determine if a set of measurements will form a triangle based on the triangle inequality theorem, we need to check if the sum of any two sides is greater than the third side for all three sides.
1. For the measurements 9, 4, 3:
9 + 4 = 13 > 3 (satisfies)
9 + 3 = 12 > 4 (satisfies)
4 + 3 = 7 < 9 (does not satisfy) - This set of measurements will not form a triangle.
2. For the measurements 8, 1, 7:
8 + 1 = 9 > 7 (satisfies)
8 + 7 = 15 > 1 (satisfies)
1 + 7 = 8 > 8 (satisfies) - This set of measurements will form a triangle.
3. For the measurements 12, 10, 22:
12 + 10 = 22 > 22 (does not satisfy)
12 + 22 = 34 > 10 (satisfies)
10 + 22 = 32 > 12 (satisfies) - This set of measurements will not form a triangle.
4. For the measurements 2, 7, 6:
2 + 7 = 9 > 6 (satisfies)
2 + 6 = 8 < 7 (does not satisfy)
7 + 6 = 13 > 2 (satisfies) - This set of measurements will not form a triangle.
Therefore, the only group of measurements that will form a triangle is 8, 1, 7.
Apply the triangle inequality theorum and determain which group of measurements will form a triangle(1point)
9,4,3
8,1,7
12,10,22
2,7,6
1 answer
1 answer