Apply the triangle inequality theorem and determine which option would be the third side of a triangle if the first shoe size measure 4 and 6

Answer 1

To apply the triangle inequality theorem, we need to determine if the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Let's consider the shoe sizes as side lengths of a potential triangle:

First shoe size: 4
Second shoe size: 6

We can now calculate the possible lengths for the third side using the triangle inequality theorem.

1) The sum of the first shoe size (4) and the second shoe size (6) is 4 + 6 = 10. To form a triangle, the third side must be greater than 10.

Possible options for the third side are greater than 10 units.

For example, if the third side measures 11, then 4 + 6 = 10 is less than 11 and satisfies the triangle inequality theorem.

However, if the third side measures something like 9, then 4 + 6 = 10 is greater than 9, and the triangle inequality theorem is not satisfied.

Therefore, any option greater than 10 can be the third side of a triangle in this case.