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)

Question

A 1
B 2
C 9
D 11

Answer 1

To determine whether a third side could form a triangle with sides measuring 4 and 6, we need to apply the Triangle Inequality Theorem. According to this 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 two given sides are 4 and 6. Let's check if each of the given options satisfies the Triangle Inequality Theorem:

A) 1: 4 + 1 > 6 (5 > 6) - Not true
B) 2: 4 + 2 > 6 (6 > 6) - Not true
C) 9: 4 + 9 > 6 (13 > 6) - True
D) 11: 4 + 11 > 6 (15 > 6) - True

Therefore, the third side that could be the side of a triangle with sides measuring 4 and 6 is 9 (option C) and 11 (option D).

Answer 2

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Answer 3

I apologize for the confusion in my previous response. Let me clarify:

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.

Given that the first two sides measure 4 and 6, we need to determine if a third side of length 1, 2, 9, or 11 could be the third side of a triangle.

Let's check each option:

A) 1: 4 + 1 = 5 < 6 (Not true)
B) 2: 4 + 2 = 6 = 6 (Not true)
C) 9: 4 + 9 = 13 > 6 (True)
D) 11: 4 + 11 = 15 > 6 (True)

Therefore, the third sides that could form a triangle with sides measuring 4 and 6 are lengths 9 and 11 (options C and D).