Question

apply the triangle inequality theorem to determine which threw side lengths for a triangle.

8, 4 and 12
10, 20 and 15
20, 10 and 30
8, 8 and 20

Answer 1

8, 4 and 12:
8 + 4 > 12
4 + 12 > 8
8 + 12 > 4

Therefore, a triangle can be formed with sides of lengths 8, 4, and 12.

10, 20 and 15:
10 + 20 > 15
20 + 15 > 10
10 + 15 > 20

Therefore, a triangle can be formed with sides of lengths 10, 20, and 15.

20, 10 and 30:
20 + 10 > 30 is not true
10 + 30 > 20 is not true
20 + 30 > 10

Therefore, a triangle cannot be formed with sides of lengths 20, 10, and 30.

8, 8 and 20:
8 + 8 > 20 is not true
8 + 20 > 8
8 + 20 > 8

Therefore, a triangle cannot be formed with sides of lengths 8, 8, and 20.