a rectangle has an area of 40 square units. the length is 6 units greater than the width. what are the dimensions of the rectangle?

8 by 5
10 by 4
11 by 9
13 by 7

Question

a rectangle has an area of 40 square units. the length is 6 units greater than the width. what are the dimensions of the rectangle?

8 by 5
10 by 4
11 by 9
13 by 7

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Equations", "Factoring Quadratics" ], "new_concepts": [], "current_concepts": [ "Quadratic Equations", "Factoring Quadratics", "Area of Rectangle" ] } ## Set up the equation for the area of the rectangle $$ \begin{aligned} &\text{Let } w \text{ be the width of the rectangle.}\ &\text{Length } l = w + 6\ &\text{Area } A = w(w + 6) = 40 \end{aligned} $$ ## Solve the quadratic equation by factoring $$ \begin{aligned} &w^2 + 6w - 40 = 0\ &(w + 10)(w - 4) = 0\ &w = 4 \quad (\text{since } w > 0)\ &l = 4 + 6 = 10 \end{aligned} $$ ## Determine the dimensions $$ \begin{aligned} &\text{Dimensions: } 10 \text{ by } 4 \end{aligned} $$

8 by 5

10 by 4

11 by 9

13 by 7

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the equation for the area of the rectangle

Solve the quadratic equation by factoring

Determine the dimensions

Answer: