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.(1 point)
Responses

A. 2
B. 11
C. 9
D. 1

Answer 1

Nonsense
4+6 = 10
the third side must be smaller than 10 or the ends of the 4 and 6 together will not reach the ends of more than ten.
the third side must be more than 6-4= 2 or the 4 side + the small side will not reach the ends of the 6 and 4
C, third side = 9
2 < 9 < 10

Answer 2

According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be greater than the third side.

So, for this question:

- 4 + 6 = 10
- 10 must be greater than the third side

Looking at the options:

A. 2 is not greater than 10, so it cannot be the third side.
B. 11 is greater than 10, so it could be the third side.
C. 9 is greater than 4, but not greater than 6, so it cannot be the third side.
D. 1 is not greater than 10, so it cannot be the third side.

Therefore, option B, 11, could be the third side of a triangle if the first two sides measure 4 and 6.