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题目

解题步骤

1. Understand the question

   critiquing work
   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

2. Explanation

   Step1: Recall triangle type rule

   For sides $a \leq b \leq c$, use:

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

   Step2: Identify largest side and squares

   Largest side $c=15$, so $c^2=15^2=225$.
   Smaller sides: $10^2=100$, $11^2=121$.
   Sum: $10^2 + 11^2 = 100 + 121 = 221$

   Step3: Compare values

   $225 > 221$, so $15^2 > 10^2 + 11^2$.

   Step4: Evaluate Ella's work

   Ella used $10^2$ vs $11^2+15^2$ (wrong sides), then incorrectly concluded acute. Her procedure and conclusion are wrong.

3. Final answer

   Ella's procedure and conclusion are incorrect.

答案

Question Analysis

OCR Text

critiquing work
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

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