To determine the classification of a triangle with side lengths [tex]\(6 \, \text{cm}\)[/tex], [tex]\(10 \, \text{cm}\)[/tex], and [tex]\(12 \, \text{cm}\)[/tex], we need to use the properties of triangle sides and the Pythagorean theorem.
### Step-by-Step Solution:
1. Calculate the squares of the side lengths:
[tex]\[
6^2 = 36
\][/tex]
[tex]\[
10^2 = 100
\][/tex]
[tex]\[
12^2 = 144
\][/tex]
2. Use the Pythagorean theorem to check the type of triangle:
- For an obtuse triangle, the square of the longest side should be greater than the sum of the squares of the other two sides.
[tex]\[
6^2 + 10^2 < 12^2
\][/tex]
[tex]\[
36 + 100 < 144
\][/tex]
[tex]\[
136 < 144
\][/tex]
This inequality is true, indicating that the triangle is obtuse.
3. Therefore, the classification that best represents the triangle is:
[tex]\[
\text{obtuse, because } 6^2 + 10^2 < 12^2
\][/tex]
### Conclusion:
The triangle with side lengths [tex]\(6 \, \text{cm}\)[/tex], [tex]\(10 \, \text{cm}\)[/tex], and [tex]\(12 \, \text{cm}\)[/tex] is best classified as an obtuse triangle. The correct statement is:
[tex]\[
\text{Obtuse, because } 6^2 + 10^2 < 12^2
\][/tex]
