1. **State the problem:** Determine the type of triangle with side lengths 10, 11, and 15. 2. **Identify the sides:** The sides are $10$, $11$, and $15$. We apply the triangle classification rules using the Pythagorean theorem: - Calculate the squares: $10^2 = 100$, $11^2 = 121$, $15^2 = 225$. 3. **Sum of squares of smaller sides:** $100 + 121 = 221$. 4. **Compare the largest side squared with the sum:** - $225$ (largest side squared) compared to $221$ (sum of smaller sides squared). 5. **Interpretation:** Since $225 > 221$, according to the Pythagorean inequality: - If $c^2 = a^2 + b^2$ it is a right triangle. - If $c^2 < a^2 + b^2$ it is an acute triangle. - If $c^2 > a^2 + b^2$ it is an obtuse triangle. Because $225 > 221$, the triangle is obtuse. 6. **Check Ella's work:** - Ella wrote: $102 ?? 112 + 152$ (probably meaning $10^2 ?? 11^2 + 15^2$), then $100 ?? 121 + 225$, then $100 < 346$. - Ella mistakenly calculated $11^2 + 15^2 = 121 + 225 = 346$ and compared $100$ to $346$. - But the largest side is 15, so $15^2 = 225$ should be compared to $10^2 + 11^2 = 221$. - Ella compared the smallest side squared to the sum of the other two squared, which is incorrect. 7. **Conclusion:** Ella's procedure is incorrect because she compared the wrong sides. Her conclusion that the triangle is acute is incorrect; it should be obtuse. **Final answer:** Ella’s procedure and conclusion are incorrect.