in triangle nlm, point s is the centroid, $qs = (3x - 5)\text{ cm}$, and $ns = (4x)\text{ cm}$.

what is ns?

$5\text{ cm}$
$10\text{ cm}$
$20\text{ cm}$
$30\text{ cm}$

Question

in triangle nlm, point s is the centroid, $qs = (3x - 5)\text{ cm}$, and $ns = (4x)\text{ cm}$.

what is ns?

$5\text{ cm}$
$10\text{ cm}$
$20\text{ cm}$
$30\text{ cm}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Centroid Theorem" ], "new_concepts": [], "current_concepts": [ "Centroid Theorem", "Median of a Triangle" ] } ## Set up the centroid relationship $$ \begin{aligned} &NS = 2 \cdot QS\ &4x = 2(3x - 5) \end{aligned} $$ ## Solve for x $$ \begin{aligned} &4x = 6x - 10\ &2x = 10\ &x = 5 \end{aligned} $$ ## Calculate NS $$ \begin{aligned} &NS = 4x\ &NS = 4(5) = 20\text{ cm} \end{aligned} $$

(A) 5 cm

(B) 10 cm

(C) 20 cm

(D) 30 cm

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the centroid relationship

Solve for x

Calculate NS

Answer: