Question

Apply the Triangle Inequality Theorum and determine which option could be the third side of a triangle if the first two sides measure 4 and 6.

A. 1
B. 11
C. 9
D. 2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the third side of a triangle, we need to check if it follows the Triangle Inequality Theorem. According to 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.

Let's check each option:

A. 1: The sum of the first two sides (4 + 6) is 10. Since 1 is less than 10, it does not satisfy the Triangle Inequality Theorem.

B. 11: The sum of the first two sides (4 + 6) is 10. Since 11 is greater than 10, it satisfies the Triangle Inequality Theorem.

C. 9: The sum of the first two sides (4 + 6) is 10. Since 9 is less than 10, it does not satisfy the Triangle Inequality Theorem.

D. 2: The sum of the first two sides (4 + 6) is 10. Since 2 is less than 10, it does not satisfy the Triangle Inequality Theorem.

Therefore, the option that could be the third side of a triangle with the first two sides measuring 4 and 6 is option B: 11.