Final answer:
Ella's procedure uses the Pythagorean theorem correctly but concludes incorrectly that the triangle is acute. The correct classification, based on her calculations, should be an obtuse triangle since the sum of the squares of the shorter sides is less than the square of the longest side.
Step-by-step explanation:
The student is asked to determine the type of triangle based on its side lengths of 10, 11, and 15. Ella has used the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The equation is given by a² + b² = c². To determine the type of triangle, Ella compares 10² + 11² with 15² since if the sum of the squares of the two shorter sides equals the square of the longest side, the triangle is a right triangle. However, for an acute triangle, this sum should be greater than the square of the longest side, and for an obtuse triangle, it should be less.
Ella's procedure involves the steps: 10² < 11² + 15², 100 < 121 + 225, and 100 < 346. Because 100 is less than 346, Ella concludes it is an acute triangle. However, this conclusion is incorrect since the proper comparison for an acute triangle would require the sum of the squares of the shorter sides to be greater than the square of the longest side, not less. Therefore, the correct type of the triangle is an obtuse triangle, not an acute triangle. Ella's procedure is correct, but her conclusion is incorrect.