Apply the triangle inequality theorem and determine which option could be the 3rd side of a triangle if the first two sides measure 4 and 6.
A) 2
B) 1
C) 9
D) 11
According to the triangle inequality theorem, for a triangle with side lengths a, b, and c, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check the options one by one:
A) 2
4 + 2 > 6
This statement is true, so 2 could be the third side of a triangle.
B) 1
4 + 1 > 6
This statement is false, so 1 could not be the third side of a triangle.
C) 9
4 + 9 > 6
This statement is true, so 9 could be the third side of a triangle.
D) 11
4 + 11 > 6
This statement is true, so 11 could be the third side of a triangle.
Therefore, the third side of a triangle could be either A) 2, C) 9, or D) 11.
There is only one correct answer
Apologies for the mistake. Let's re-evaluate the options:
A) 2
4 + 2 > 6
This statement is true, so 2 could be the third side of a triangle.
C) 9
4 + 9 > 6
This statement is true, so 9 could be the third side of a triangle.
D) 11
4 + 11 > 6
This statement is true, so 11 could be the third side of a triangle.
Therefore, both options A) 2 and D) 11 could be the third side of a triangle.