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: 10² ?? 11² + 15² 100 ?? 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 correct, but her conclusion is incorrect. ○ ellas procedure is incorrect, but her conclusion is correct. ○ ellas procedure and conclusion are incorrect.

Explanation:

Step1: Recall the triangle - type determination rule

For a triangle with side lengths \(a\), \(b\), \(c\) (\(c\) is 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: Calculate the values

Calculate \(10^{2}+11^{2}=100 + 121=221\), and \(15^{2}=225\). Since \(221<225\) (i.e., \(10^{2}+11^{2}<15^{2}\)), the triangle is obtuse.

Answer:

Ella's procedure is incorrect, but her conclusion is correct.