Apply the Triangle Theorem to determine which three sides lengths form a triangle .
20,10,40
8,8,20
1020,15
8,4,12
To determine which sets of side lengths 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.
1. For the side lengths 20, 10, and 40:
20 + 10 = 30 < 40
20 + 40 = 60 > 10
10 + 40 = 50 > 20
Therefore, the side lengths 20, 10, and 40 do form a triangle.
2. For the side lengths 8, 8, and 20:
8 + 8 = 16 < 20
8 + 20 = 28 > 8
8 + 20 = 28 > 8
Therefore, the side lengths 8, 8, and 20 do form a triangle.
3. For the side lengths 10, 20, and 15:
10 + 20 = 30 < 15
10 + 15 = 25 < 20
15 + 20 = 35 > 10
Therefore, the side lengths 10, 20, and 15 do not form a triangle.
4. For the side lengths 8, 4, and 12:
8 + 4 = 12 < 12
8 + 12 = 20 > 4
4 + 12 = 16 > 8
Therefore, the side lengths 8, 4, and 12 do not form a triangle.