Answer :
To determine whether a triangle can be formed with side lengths \(4\), \(8\), and \(11\), we can use the triangle inequality theorem. This theorem states that, for any three side lengths \(a\), \(b\), and \(c\), a triangle can be formed if and only if the sum of any two sides is greater than the third side.
Let's check each condition of the triangle inequality theorem:
1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)
Given side lengths \(a = 4\), \(b = 8\), and \(c = 11\), we check the following inequalities:
1. \(4 + 8 > 11\)
[tex]\[ 12 > 11\quad \text{(True)} \][/tex]
2. \(4 + 11 > 8\)
[tex]\[ 15 > 8\quad \text{(True)} \][/tex]
3. \(8 + 11 > 4\)
[tex]\[ 19 > 4\quad \text{(True)} \][/tex]
Since all three conditions are satisfied, a triangle can be formed with side lengths \(4\), \(8\), and \(11\).
Therefore, the correct statement is:
Yes, because [tex]\(4 + 8 > 11\)[/tex].
Let's check each condition of the triangle inequality theorem:
1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)
Given side lengths \(a = 4\), \(b = 8\), and \(c = 11\), we check the following inequalities:
1. \(4 + 8 > 11\)
[tex]\[ 12 > 11\quad \text{(True)} \][/tex]
2. \(4 + 11 > 8\)
[tex]\[ 15 > 8\quad \text{(True)} \][/tex]
3. \(8 + 11 > 4\)
[tex]\[ 19 > 4\quad \text{(True)} \][/tex]
Since all three conditions are satisfied, a triangle can be formed with side lengths \(4\), \(8\), and \(11\).
Therefore, the correct statement is:
Yes, because [tex]\(4 + 8 > 11\)[/tex].
