which of the following measurements is possible for the missing side length? select all that apply.

2
10
12
9
5
3

Question

which of the following measurements is possible for the missing side length? select all that apply.

2
10
12
9
5
3

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Inequality Theorem" ], "new_concepts": [], "current_concepts": [ "Triangle Inequality Theorem" ] } ## Apply the Triangle Inequality Theorem Let the missing side length be $x$. $$ \begin{aligned} &6 - 4 < x < 6 + 4\ &2 < x < 10 \end{aligned} $$ ## Evaluate the given options $$ \begin{aligned} &x = 2 \implies 2 < 2 \quad (\text{False})\ &x = 10 \implies 10 < 10 \quad (\text{False})\ &x = 12 \implies 12 < 10 \quad (\text{False})\ &x = 9 \implies 2 < 9 < 10 \quad (\text{True})\ &x = 5 \implies 2 < 5 < 10 \quad (\text{True})\ &x = 3 \implies 2 < 3 < 10 \quad (\text{True}) \end{aligned} $$

2

10

12

9

5

3

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Inequality Theorem" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Apply the Triangle Inequality Theorem

Evaluate the given options

Answer: