Apply the triangular in e q u a l i t y t h e o r e m and determine which option could be the third side of a triangle at the first two sides measure 4 and 6 a 2 b 1 c 9 d 11
According to the triangular inequality 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 apply this theorem to the given options:
a) Option a: 2
To satisfy the triangular inequality theorem, the sum of the two sides (4 and 6) must be greater than 2. However, since 4 + 6 = 10, which is greater than 2, option a can be the third side of a triangle.
b) Option b: 1
To satisfy the triangular inequality theorem, the sum of the two sides (4 and 6) must be greater than 1. However, since 4 + 6 = 10, which is greater than 1, option b can be the third side of a triangle.
c) Option c: 9
To satisfy the triangular inequality theorem, the sum of the two sides (4 and 6) must be greater than 9. However, 4 + 6 = 10, which is not greater than 9. Therefore, option c cannot be the third side of a triangle.
d) Option d: 11
To satisfy the triangular inequality theorem, the sum of the two sides (4 and 6) must be greater than 11. However, 4 + 6 = 10, which is not greater than 11. Therefore, option d cannot be the third side of a triangle.
So, options a (2) and b (1) could be the third side of a triangle.