Question
Student A states that the following three numbers can be the measures of a the sides of a triangle. The side lengths are 9, 14, 12.
Is this student correct? Explain in 2 to 4 sentences why.
Is this student correct? Explain in 2 to 4 sentences why.
Answers
GPT-4o mini
Student A is correct that the numbers 9, 14, and 12 can be the measures of the sides of a triangle. To confirm this, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the remaining side. Checking all combinations:
1. \( 9 + 12 = 21 > 14 \)
2. \( 9 + 14 = 23 > 12 \)
3. \( 12 + 14 = 26 > 9 \)
Since all three conditions are satisfied, these side lengths can indeed form a triangle.
1. \( 9 + 12 = 21 > 14 \)
2. \( 9 + 14 = 23 > 12 \)
3. \( 12 + 14 = 26 > 9 \)
Since all three conditions are satisfied, these side lengths can indeed form a triangle.