Triangle Inequality Theorem Quick Check%0D%0A3 of 53 of 5 Items%0D%0A%0D%0AQuestion%0D%0AApply 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 11
d 9
To determine if an option could be the third side of a triangle, it must follow the Triangle Inequality Theorem, which states that 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 first two sides measure 4 and 6.
For option a: 2, 4 + 2 = 6, which is greater than 2. However, 6 - 2 = 4, which is not greater than 2. Therefore, option a cannot be the third side of a triangle.
For option b: 1, 4 + 1 = 5, which is greater than 1. However, 6 - 1 = 5, which is not greater than 1. Therefore, option b cannot be the third side of a triangle.
For option c: 11, 4 + 11 = 15, which is greater than 11. Also, 6 + 11 = 17, which is greater than 11. Therefore, option c could be the third side of a triangle.
For option d: 9, 4 + 9 = 13, which is greater than 9. Also, 6 + 9 = 15, which is greater than 9. Therefore, option d could be the third side of a triangle.
In conclusion, options c (11) and d (9) could be the third side of a triangle if the first two sides measure 4 and 6.