the length of a rectangle is three times the width. the area of the rectangle is 108 sq in. what is the width of the rectangle?

6 in.
9 in.
12 in.
36 in.

Question

the length of a rectangle is three times the width. the area of the rectangle is 108 sq in. what is the width of the rectangle?

6 in.
9 in.
12 in.
36 in.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Area Formula" ], "new_concepts": [ "Rectangle Area Formula", "Quadratic Equation Formulation" ], "current_concepts": [ "Triangle Area Formula", "Rectangle Area Formula", "Quadratic Equation Formulation" ] } ## Formulate the area equation $$ \begin{aligned} &\text{Let } w = \text{width of the rectangle (in inches)}\ &\text{Length } l = 3w\ &\text{Area } A = l \times w = 3w^2\ &3w^2 = 108 \end{aligned} $$ ## Solve for the width $$ \begin{aligned} &w^2 = \frac{108}{3}\ &w^2 = 36\ &w = 6 \quad (w > 0) \end{aligned} $$

(A) 6 in

(B) 9 in

(C) 12 in

(D) 36 in

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Rectangle Area Formula" ] }

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Question

Explanation:

Formulate the area equation

Solve for the width

Answer: