(PICK ONE)
(don't pick 2 or 3 or all of them only pick one idiot bot)
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.
A. 2
B. 1
C. 9
D. 11
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.
For the given scenario, if the first two sides measure 4 and 6, then the sum of their lengths is 4+6=10.
To be a valid third side of a triangle, the length of the third side must be greater than 10- the sum of the two given sides.
Let's evaluate each option:
A. 2: The length of this side is 2, which is less than 10- therefore, it cannot be the third side of a triangle.
B. 1: Similar to option A, the length of this side is also 1, which is less than 10- so it cannot be the third side of a triangle.
C. 9: The length of this side is 9, which is equal to 10- which satisfies the Triangle Inequality Theorem. Therefore, option C could be the third side of a triangle.
D. 11: The length of this side is 11, which is greater than 10- so it satisfies the Triangle Inequality Theorem. Therefore, option D could also be the third side of a triangle.
So, both options C and D could be the third side of a triangle.