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
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.
In this case, the first two sides measure 4 and 6. To satisfy the Triangle Inequality Theorem, the third side must be such that:
4 + 6 > Third side length
And
6 + Third side length > 4
Simplifying these inequalities, we get:
10 > Third side length
And
6 > Third side length - 4
Combining these inequalities gives us:
10 > Third side length > 2
Based on the given options, the only number that falls within this range is 9. Therefore, 9 is the only option that could be the third side of a triangle, given that the first two sides measure 4 and 6.
is the answer 2 or 1
Apologies for the confusion in the previous response. If the first two sides measure 4 and 6, the third side length must satisfy the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
For this scenario, we have:
4 + 6 > Third side length
10 > Third side length
Based on this, the only option that is less than 10 is 9. Therefore, 9 is the only option that could be the third side of a triangle, given that the first two sides measure 4 and 6.