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

Explanation:

Step1: Recall triangle type rule

For a triangle with sides $a \leq b \leq c$, 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 $15^2$ vs $10^2+11^2$

Step3: Calculate each side squared

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

Step4: Compare values

$225 > 221$, so triangle is obtuse. Ella used wrong side for comparison, and her conclusion is wrong.

Answer:

Ella's procedure and conclusion are incorrect.