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: 11
b: 9
c: 2
D: 1
To determine which option could be the third side of a triangle, we need to apply the Triangle Inequality Theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check each option:
a: 11: If the first two sides measure 4 and 6, their sum is 4 + 6 = 10. Since 10 is less than 11, option a (11) could be the third side of a triangle.
b: 9: The sum of the first two sides is 4 + 6 = 10. Since 10 is greater than 9, option b (9) could NOT be the third side of a triangle.
c: 2: The sum of the first two sides is 4 + 6 = 10. Since 10 is greater than 2, option c (2) could NOT be the third side of a triangle.
D: 1: The sum of the first two sides is 4 + 6 = 10. Since 10 is greater than 1, option D (1) could NOT be the third side of a triangle.
Therefore, the option that could be the third side of a triangle is option a: 11.