To determine if the three side lengths 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.
1. For the side lengths 20, 10, 30:
20 + 10 = 30 > 30 (satisfied)
20 + 30 = 50 > 10 (satisfied)
10 + 30 = 40 > 20 (satisfied)
These side lengths form a triangle.
2. For the side lengths 8, 8, 20:
8 + 8 = 16 < 20 (not satisfied)
8 + 20 = 28 > 8 (satisfied)
8 + 20 = 28 > 8 (satisfied)
These side lengths do not form a triangle.
3. For the side lengths 8, 4, 12:
8 + 4 = 12 < 12 (not satisfied)
8 + 12 = 20 > 4 (satisfied)
4 + 12 = 16 > 8 (satisfied)
These side lengths do not form a triangle.
4. For the side lengths 10, 20, 15:
10 + 20 = 30 > 15 (satisfied)
10 + 15 = 25 > 20 (satisfied)
20 + 15 = 35 > 10 (satisfied)
These side lengths form a triangle.
Therefore, the side lengths 20, 10, 30 and 10, 20, 15 form triangles, while 8, 8, 20 and 8, 4, 12 do not.
Apply the triangle inequality theorem to determine which three side lengths form a triangle
20,10,30
8,8,20
8,4,12
10,20,15
1 answer