Question

Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point) Responses
A, 8, 8, 20
B, 20, 10, 30
C, 10, 20, 15
D, 8, 4, 12

Answer 1

You can only pick one.

Answer 2

Based on the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

A) 8 + 8 > 20, 8 + 20 > 8, but 8 + 20 < 8. Therefore, A does not form a triangle.
B) 20 + 10 > 30, 10 + 30 > 20, and 20 + 30 > 10. Therefore, B forms a triangle.
C) 10 + 20 > 15, 20 + 15 > 10, and 10 + 15 > 20. Therefore, C forms a triangle.
D) 8 + 4 > 12, 4 + 12 > 8, and 8 + 12 > 4. Therefore, D forms a triangle.

Therefore, sides B, C, and D form a triangle.

Answer 3

In that case, based on the Triangle Inequality Theorem, the triangle would be formed by Side C with lengths 10, 20, and 15.