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
2
2
11
11
9
9
1
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the first two sides measure 4 and 6.
To determine which option could be the third side of a triangle, we need to find a value that is greater than the difference between the lengths of the first two sides (6 - 4 = 2) but less than their sum (4 + 6 = 10).
From the given options, the values that satisfy this condition are 2 and 9.
Therefore, the possible choices for the third side of the triangle are 2 and 9.
one
If the first two sides measure 4 and 6, and you are given the option "one" as a possible third side, it is not enough information to determine if "one" could be the third side of a triangle.
To determine if "one" could be the third side, we need to compare it to the difference between the lengths of the first two sides (6 - 4 = 2) and their sum (4 + 6 = 10).
Since "one" is less than the difference of 2 and less than the sum of 10, it could be the third side of a triangle.
one answer
Apologies for the confusion. If "one" is the only available option as the third side and the first two sides measure 4 and 6, then "one" cannot be the third side of a triangle.
According to the Triangle Inequality Theorem, the third side must be greater than the difference between the lengths of the first two sides and less than their sum. In this case, the difference between 4 and 6 is 2, and their sum is 10. Since "one" is less than 2, it does not satisfy the Triangle Inequality Theorem and cannot be the third side of a triangle.