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
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According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
So, if the first two sides of the triangle measure 4 and 6, we need to determine which option is greater than 2 but less than 10.
Let's list the options and check for each one:
1. 3
2. 7
3. 10
4. 2
For option 1: 4 + 3 = 7, which is greater than 6. However, 3 is not greater than 4. So, option 1 cannot be the third side of the triangle.
For option 2: 4 + 7 = 11, which is greater than 6. However, 7 is not greater than 4. So, option 2 cannot be the third side of the triangle.
For option 3: 4 + 10 = 14, which is greater than 6. Also, 10 is greater than 4. So, option 3 can be the third side of the triangle.
For option 4: 4 + 2 = 6, which is not greater than 6. So, option 4 cannot be the third side of the triangle.
Therefore, the only option that could be the third side of a triangle with the first two sides measuring 4 and 6 is option 3, which measures 10.