Final answer:
The side lengths 11, 20, and 35 cannot form a triangle because they do not satisfy the Triangle Inequality Theorem; the sum of any two sides must be greater than the third side, and 11 + 20 is not greater than 35.
Step-by-step explanation:
To determine if the side lengths 11, 20, and 35 can form a triangle, we can use the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. To check if a triangle can be formed with the given side lengths, we can apply this principle:
- Check if 11 + 20 > 35: The sum is 31, which is not greater than 35.
- Check if 11 + 35 > 20: The sum is 46, which is greater than 20.
- Check if 20 + 35 > 11: The sum is 55, which is greater than 11.
Since one of the conditions failed (11 + 20 is not greater than 35), the side lengths 11, 20, and 35 cannot form a triangle.