Question

A triangle has side lengths of 13.5 and 17. Which of the following COULD be the length of the third side. (Select all that apply).

31
30
3
D8
5
3.5

Answer 1

The possible lengths of the third side are 30, 3, and 3.5.

Step-by-step explanation:

To determine the possible length of the third side of a triangle with side lengths 13.5 and 17, we need to apply the triangle inequality theorem.

According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we can eliminate any options that don't satisfy this rule.

Let's check each option:

• 31: 13.5 + 17 = 30.5 < 31 (Not possible)
• 30: 13.5 + 17 = 30.5 > 30 (Possible)
• 3: 13.5 + 3 = 16.5 > 3 (Possible)
• D8: This option is not a number, so it cannot be the length of a side in a triangle.
• 5: 13.5 + 5 = 18.5 > 5 (Possible)
• 3.5: 13.5 + 3.5 = 17 > 3.5 (Possible)

Based on the triangle inequality theorem, the possible lengths of the third side are 30, 3, and 3.5.