21) find a simplified algebraic expression for the perimeter and area of the rectangle below.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Algebraic Expressions", "Algebraic Simplification" ], "new_concepts": [ "Perimeter of a Rectangle", "Area of a Rectangle" ], "current_concepts": [ "Algebraic Expressions", "Algebraic Simplification", "Perimeter of a Rectangle", "Area of a Rectangle" ] } ## Calculate the perimeter of the rectangle $$ \begin{aligned} P &= 2(\text{length} + \text{width}) \ P &= 2((2x - 6) + 4x) \ P &= 2(6x - 6) \ P &= 12x - 12 \end{aligned} $$ ## Calculate the area of the rectangle $$ \begin{aligned} A &= \text{length} \times \text{width} \ A &= (2x - 6)(4x) \ A &= 8x^2 - 24x \end{aligned} $$ Perimeter: $12x - 12$ Area: $8x^2 - 24x$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Area and Perimeter of Rectangles" ] }

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Calculate the perimeter of the rectangle

Calculate the area of the rectangle

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