Question

Given three side lengths 9, 13, and 19:

Complete the following statements, using:

I. 9 + 13 = 19
II. 9 + 19 = 13
III. 13 + 19 = 9

A) I, II, III
B) I, III
C) II, III
D) I, II

Answer 1

None of the statements I, II, or III are true because each set of side lengths violates the triangle inequality theorem.

Step-by-step explanation:

The question is about triangle inequality, 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. Looking at the given side lengths of 9, 13, and 19, we can see that:

• 9 + 13 = 22, which is greater than 19
• 9 + 19 = 28, which is greater than 13
• 13 + 19 = 32, which is greater than 9

Therefore, none of the statements I, II, or III are true. They would imply that you can have sides of a triangle which don't adhere to the triangle inequality, but in fact, all sets of side lengths given must obey the triangle inequality for a triangle to exist.