To determine if the three side lengths form a triangle, we need to check if the sum of the two smaller side lengths is greater than the largest side length for each set of side lengths.
1. For the side lengths 8, 4, and 12:
- 8 + 4 = 12 > 12; 4 + 12 = 16 > 8; 8 + 12 = 20 > 4
- This set of side lengths forms a triangle.
2. For the side lengths 20, 10, and 30:
- 20 + 10 = 30 = 30; 10 + 30 = 40 > 20; 20 + 30 = 50 > 10
- This set of side lengths forms a triangle.
3. For the side lengths 10, 20, and 15:
- 10 + 15 = 25 > 20; 20 + 15 = 35 > 10; 10 + 20 = 30 > 15
- This set of side lengths forms a triangle.
4. For the side lengths 8, 8, and 20:
- 8 + 8 = 16 < 20
- This set of side lengths does not form a triangle since the sum of the two smaller side lengths is not greater than the largest side length.
Therefore, the sets of side lengths that form a triangle are 8, 4, and 12; 20, 10, and 30; and 10, 20, and 15.
Apply the triangle inequality THEOREN to determine which three side links form a triangle
8,4,12
20,10,30
10,20,15
8,8,20
1 answer
1 answer