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.(1 point)
Responses
11
11
1
1
2
2
9
9
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 third side.
Applying this theorem to the given options:
- Option 11: This does not satisfy the Triangle Inequality Theorem. 4 + 6 = 10, which is less than 11.
- Option 1: This does not satisfy the Triangle Inequality Theorem. 4 + 6 = 10, which is greater than 1.
- Option 2: This satisfies the Triangle Inequality Theorem. 4 + 6 = 10, which is greater than 2.
- Option 9: This satisfies the Triangle Inequality Theorem. 4 + 6 = 10, which is greater than 9.
Therefore, the third side of a triangle could be 2 or 9, according to the given options.
whats the answer you think?
Based on the Triangle Inequality Theorem, the third side of a triangle must have a length that is greater than the difference between the lengths of the other two sides, but less than the sum of their lengths.
In this case, the first two sides measure 4 and 6.
The difference between the lengths of the two sides is 6 - 4 = 2.
So, the third side must have a length greater than 2 but less than 10.
Out of the given options, the only one that falls within this range is 9.
Therefore, the third side that could form a triangle with sides of length 4 and 6 is 9.