for a craft project, four students each chose three pieces of wire from a box.

dons wires measure 3 inches, 5 inches, and 12 inches.
margos wires measure 6 inches, 8 inches, and 14 inches.
sonjis wires measure 12 inches, 8 inches, and 17 inches.
liams wires measure 16 inches, 8 inches, and 27 inches.

which student chose pieces that can be used to construct a triangle?

don
margo
sonji
liam

Question

for a craft project, four students each chose three pieces of wire from a box.

dons wires measure 3 inches, 5 inches, and 12 inches.
margos wires measure 6 inches, 8 inches, and 14 inches.
sonjis wires measure 12 inches, 8 inches, and 17 inches.
liams wires measure 16 inches, 8 inches, and 27 inches.

which student chose pieces that can be used to construct a triangle?

don
margo
sonji
liam

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Triangle Inequality Theorem" ], "new_concepts": [], "current_concepts": [ "Triangle Inequality Theorem" ] } ## Apply the Triangle Inequality Theorem Using the *Triangle Inequality Theorem* knowledge point $$ \begin{aligned} &\text{For any triangle with side lengths } a, b, c \text{ (where } a \le b \le c\text{):}\ &a + b > c \end{aligned} $$ ## Evaluate Don's side lengths Using the *Triangle Inequality Theorem* knowledge point $$ \begin{aligned} &\text{Side lengths: } 3, 5, 12\ &3 + 5 = 8 \le 12 \end{aligned} $$ ## Evaluate Margo's side lengths Using the *Triangle Inequality Theorem* knowledge point $$ \begin{aligned} &\text{Side lengths: } 6, 8, 14\ &6 + 8 = 14 \le 14 \end{aligned} $$ ## Evaluate Sonji's side lengths Using the *Triangle Inequality Theorem* knowledge point $$ \begin{aligned} &\text{Side lengths: } 8, 12, 17\ &8 + 12 = 20 > 17 \end{aligned} $$ ## Evaluate Liam's side lengths Using the *Triangle Inequality Theorem* knowledge point $$ \begin{aligned} &\text{Side lengths: } 8, 16, 27\ &8 + 16 = 24 \le 27 \end{aligned} $$

Don

Margo

Sonji

Liam

{ "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 Don's side lengths

Evaluate Margo's side lengths

Evaluate Sonji's side lengths

Evaluate Liam's side lengths

Answer: