state if the triangle is right, acute, or obtuse.
write your answers in the form sqrt(____) with no spaces.
identify the variables.
$a =$
$b = 2\sqrt{2}$
$c =$

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Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Radical Simplification", "Triangle Side Lengths" ], "current_concepts": [ "Radical Simplification", "Triangle Side Lengths" ] } ## Identify the side lengths of the triangle $$ \begin{aligned} &\text{Given side lengths: } 2, \quad 2\sqrt{2}, \quad 2\sqrt{3} \end{aligned} $$ ## Convert side lengths to the form $\sqrt{x}$ $$ \begin{aligned} &a = 2 = \sqrt{4} \ &b = 2\sqrt{2} = \sqrt{4 \times 2} = \sqrt{8} \ &c = 2\sqrt{3} = \sqrt{4 \times 3} = \sqrt{12} \end{aligned} $$ ## Format the answers as requested $$ \begin{aligned} &a = \text{sqrt(4)} \ &c = \text{sqrt(12)} \end{aligned} $$ ## Question 1 $a =$ sqrt(4) ## Question 2 $c =$ sqrt(12) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Radical Simplification" ] }

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Question

Explanation:

Identify the side lengths of the triangle

Convert side lengths to the form \(\sqrt{x}\)

Format the answers as requested

Answer:

Question 1

Question 2