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? \bigcirc ellas procedure and conclusion are correct. \bigcirc ellas procedure is correct, but her conclusion is incorrect. \bigcirc ellas procedure is incorrect, but her conclusion is correct. \bigcirc ellas procedure and conclusion are incorrect.

Explanation:

Step1: Recall triangle type rule

For a triangle with side lengths $a \leq b \leq c$, use:

• $c^2 = a^2 + b^2$: Right triangle
• $c^2 < a^2 + b^2$: Acute triangle
• $c^2 > a^2 + b^2$: Obtuse triangle

Step2: Identify longest side

Longest side $c=15$, so compare $15^2$ to $10^2+11^2$.

Step3: Calculate each term

$15^2 = 225$, $10^2+11^2=100+121=221$

Step4: Compare values

$225 > 221$, so triangle is obtuse.

Step5: Analyze Ella's work

Ella used shortest side instead of longest, and conclusion is wrong.

Answer:

Ella's procedure and conclusion are incorrect.