Question
Apply the Triangle Inequality Theorem and determine which option could be the third side of a triangle if the first two sides measure 4 and 6.
A. 2
B. 1
C. 9
Answers
Answered by
GPT 3.5
According to the Triangle Inequality Theorem, for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, we have the first two sides measuring 4 and 6.
So, we need to check if the sum of these two sides is greater than the length of the third side for each option.
Option A: 4 + 6 > 2, which is true.
Option B: 4 + 6 > 1, which is true.
Option C: 4 + 6 > 9, which is false.
Based on the Triangle Inequality Theorem, option C (9) cannot be the third side of a triangle with first two sides measuring 4 and 6.
Therefore, the correct answer is:
B. 1
In this case, we have the first two sides measuring 4 and 6.
So, we need to check if the sum of these two sides is greater than the length of the third side for each option.
Option A: 4 + 6 > 2, which is true.
Option B: 4 + 6 > 1, which is true.
Option C: 4 + 6 > 9, which is false.
Based on the Triangle Inequality Theorem, option C (9) cannot be the third side of a triangle with first two sides measuring 4 and 6.
Therefore, the correct answer is:
B. 1
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