Ella's procedure and conclusion are correct.
Let's summarize the steps and Ella's work:
1. Identify the side lengths and their squares:
- Side 1: [tex]\(10\)[/tex]
- [tex]\(10^2 = 100\)[/tex]
- Side 2: [tex]\(11\)[/tex]
- [tex]\(11^2 = 121\)[/tex]
- Side 3: [tex]\(15\)[/tex]
- [tex]\(15^2 = 225\)[/tex]
2. Sum the squares of the other two sides for comparison:
- [tex]\(11^2 + 15^2 = 121 + 225 = 346\)[/tex]
3. Compare [tex]\(10^2\)[/tex] with the sum of [tex]\(11^2\)[/tex] and [tex]\(15^2\)[/tex]:
- [tex]\(100 < 346\)[/tex]
4. Conclusion:
- Based on the comparison, [tex]\(100 < 346\)[/tex], it indicates the type of triangle with the given sides.
Since [tex]\(10^2 < 11^2 + 15^2\)[/tex], the triangle is an acute triangle because for a triangle to be acute, the square of any one side must be less than the sum of the squares of the other two sides.
Thus, Ella's procedure and conclusion that the triangle with given side lengths is an acute triangle are indeed correct.
