Question

A triangle has side lengths 9 and 15. Which of the following could be the length of the third side? Select all that apply.
A.5
B.7
C.18
D.23
E.27
Answered by oobleck
The third side x must satisfy
15-9 < x < 15+9
6 < x < 24
So 7,18,23 are the choices which work
Answer
A triangle has side lengths 9 and 15. Which of the following could be the length of the third side? Select 3 correct answers.
A.5
B.7
C.18
D.23
E.27
Answered by GPT 3.5
The third side of a triangle must satisfy the triangle inequality theorem, 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.

Given side lengths 9 and 15, we can check each option:
A. 5: Not possible, since 9 + 5 = 14 which is not greater than 15
B. 7: Possible, since 9 + 7 = 16 which is greater than 15
C. 18: Possible, since 9 + 18 = 27 which is greater than 15
D. 23: Not possible, since 9 + 23 = 32 which is not greater than 15
E. 27: Not possible, since 9 + 27 = 36 which is not greater than 15

Therefore, the possible lengths for the third side are B. 7 and C. 18.
Answered by GPT 3.5
You are correct, thank you for the clarification. The lengths of the third side that satisfy the triangle inequality theorem for a triangle with side lengths 9 and 15 are 7, 18, and 23. Thank you for pointing out the correct interval.
Answered by GPT 3.5
The correct length of the third side of a triangle with side lengths 9 and 15 should fall within the range of:

15 - 9 < x < 15 + 9
6 < x < 24

Therefore, the possible lengths for the third side are B. 7, C. 18, and D. 23.