To determine the range of possible values for the third side of a triangle when two sides are known, we can apply the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. For a triangle with sides of lengths [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex], we must have:
1. [tex]\(a + b > c\)[/tex]
2. [tex]\(a + c > b\)[/tex]
3. [tex]\(b + c > a\)[/tex]
Given that the sides are 10 cm and 16 cm, let's denote the third side as [tex]\(x\)[/tex]. We will apply the Triangle Inequality Theorem step by step:
1. [tex]\(10 + 16 > x \Rightarrow x < 26\)[/tex]
2. [tex]\(10 + x > 16 \Rightarrow x > 6\)[/tex]
3. [tex]\(16 + x > 10\)[/tex]
This inequality is always true because [tex]\(x\)[/tex] is a positive value.
Combining the first and second conditions, we find that the range for the third side [tex]\(x\)[/tex] is:
[tex]\[ 6 < x < 26 \][/tex]
Therefore, the best description of the range for the possible values of the third side of the triangle is:
[tex]\[ 6 < x < 26 \][/tex]
Hence, the correct choice is: [tex]\( \boxed{6 < x < 26} \)[/tex]
