To determine if it is possible to form a triangle with side lengths of 5, 5, and 10, we use the Triangle Inequality Theorem. This theorem states that for three sides to form a triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
Let's check each condition:
1. First condition:
[tex]\[ 5 + 5 > 10 \][/tex]
[tex]\[ 10 > 10 \][/tex]
This is not true because 10 is not greater than 10.
2. Second condition:
[tex]\[ 5 + 10 > 5 \][/tex]
[tex]\[ 15 > 5 \][/tex]
This is true because 15 is greater than 5.
3. Third condition:
[tex]\[ 5 + 10 > 5 \][/tex]
[tex]\[ 15 > 5 \][/tex]
This is also true because 15 is greater than 5.
For the side lengths to form a triangle, all three conditions must be satisfied. In this case, the first condition is not satisfied.
Since not all conditions are met, it is not possible to form a triangle with side lengths of 5, 5, and 10.
The correct answer is:
B. False
