the length of a rectangle is 4 centimeters less than three times its width. its area is 15 square centimeters. find the dimensions of the rectangle.

the width is cm.
the length is cm.

Question

the length of a rectangle is 4 centimeters less than three times its width. its area is 15 square centimeters. find the dimensions of the rectangle.

the width is   cm.
the length is   cm.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Geometric Word Problems", "Area Calculations", "Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Geometric Word Problems", "Area Calculations", "Quadratic Equations" ] } ## Formulate the quadratic equation $$ \begin{aligned} &\text{Let } w \text{ be the width in cm.}\ &\text{Length } l = 3w - 4\ &\text{Area } A = w(3w - 4) = 15\ &3w^2 - 4w - 15 = 0 \end{aligned} $$ ## Solve for the width $$ \begin{aligned} &(3w + 5)(w - 3) = 0\ &w = 3 \quad (\text{since } w > 0) \end{aligned} $$ ## Calculate the length $$ \begin{aligned} &l = 3(3) - 4 = 5 \end{aligned} $$ The length of a rectangle is 4 centimeters less than three times its width. Its area is 15 square centimeters. Find the dimensions of the rectangle. The width is 3 cm. The length is 5 cm. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Formulate the quadratic equation

Solve for the width

Calculate the length

Answer: