Question

ellas geometry teacher asked each student to devise a problem and write out its solution. here is ellas work: a triangle has side lengths of 10, 11, and 15. what type of triangle is it? procedure: 10^2 ? 11^2 + 15^2 100 ? 121 + 225 100 < 346 conclusion: this triangle is an acute triangle. which statement best summarizes ellas work? ellas procedure and conclusion are correct. ellas procedure is incorrect, but her conclusion is correct. ellas procedure is correct, but her conclusion is incorrect. ellas procedure and conclusion are incorrect.

Explanation:

Step1: Recall the Pythagorean - related rule for triangles

For a triangle with side lengths \(a\), \(b\), and \(c\) (\(c\) being the longest side), if \(a^{2}+b^{2}>c^{2}\), the triangle is acute; if \(a^{2}+b^{2}=c^{2}\), the triangle is right - angled; if \(a^{2}+b^{2}

Step2: Identify the longest side and calculate

The side lengths are \(10\), \(11\), and \(15\). Here \(c = 15\), \(a = 10\), \(b = 11\). Calculate \(a^{2}+b^{2}=10^{2}+11^{2}=100 + 121=221\) and \(c^{2}=15^{2}=225\). Since \(10^{2}+11^{2}=221<225 = 15^{2}\), the triangle is obtuse.

Step3: Analyze Ella's work

Ella calculated \(10^{2}+11^{2}+15^{2}\) in a wrong - way. She should have compared \(10^{2}+11^{2}\) with \(15^{2}\). Her procedure is incorrect. And her conclusion that the triangle is acute is also incorrect.

Answer:

Ella's procedure and conclusion are incorrect.