Ella’s geometry teacher asked each student to devise a problem and write out its solution. Here is Ella’s work: A triangle has side lengths of 10, 11, and 15. What type of triangle is it? Procedure: 102 ?? 112 + 152 100 ?? 121 + 225 100 < 346 Conclusion: This triangle is an acute triangle. Which statement best summarizes Ella’s work? Ella’s procedure and conclusion are correct. Ella’s procedure is correct, but her conclusion is incorrect. Ella’s procedure is incorrect, but her conclusion is correct. Ella’s procedure and conclusion are incorrect.

As by the converse of Pythagoras: In a triangle with side lengths a, b, and c where c is the length of the longest side, if [tex]c^2<a^2+b^2[/tex] then the triangle is acute.

To find the triangle acute or not the procedure should be followed is

[tex]15^2=225[/tex]

[tex]10^2+11^2=100+121=221[/tex]

which shows [tex]c^2>a^2+b^2[/tex].

Hence, the triangle is obtuse not acute

∴ Ella’s procedure and conclusion are incorrect.

snehashish65 snehashish65 · Answer 2 · 2021-11-10T10:41:11+01:00

The Ella's procedure and conclusion are incorrect to obtain the type of given triangle.

Given data:

The length of sides of triangle are, 10 units, 11 units and 15 units.

The type of triangle can be determined by applying the converse of Pythagoras theorem.

According to converse of Pythagoras theorem, "The triangle having the side a, b and c , such that the square of third side should be less than sum of square of other two sides of triangle, then the triangle is acute". This implies,

[tex]c^{2}<a^{2}+b^{2}[/tex]

Then,

[tex]c^{2}<a^{2}+b^{2}\\15^{2}<10^{2}+11^{2}\\225<100+121\\225<221[/tex]

The above condition is not satisfied for the acute triangle. Hence, the given triangle cannot be acute.

Thus, we can conclude that the neither Ella's procedure is correct, nor the conclusion is correct to identify the type of triangle.

Learn more about the acute triangle here:

https://brainly.com/question/10388714