Question

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

Answer 1

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.