The problem is asking if there is a triangle with side lengths of 9, 11, and an unknown number. To determine if this triangle can exist, I need to apply the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.
To answer this question, I will start by checking if 9 + 11 is greater than the third side. 9 + 11 equals 20. Now I will compare this sum to the unknown side length. If the unknown side length is less than or equal to 20, then a triangle can exist. However, if the unknown side length is greater than 20, a triangle cannot exist.
In this case, I need to pick an unknown number that is greater than 20. So my answer is:
9, 11 , 21
This answer makes sense because the sum of 9 + 11 is equal to 20, and any triangle with two sides of lengths 9 and 11 would require the third side to be longer than 20. Therefore, a triangle with side lengths of 9, 11, and 21 cannot exist.