type the answer in the box, using whole numbers.

q. the perimeter of the rectangle is 64. find $a$.

Question

type the answer in the box, using whole numbers.

q. the perimeter of the rectangle is 64. find $a$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Perimeter of Quadrilaterals", "Solving Multi-Step Equations" ], "new_concepts": [], "current_concepts": [ "Perimeter of Quadrilaterals", "Solving Multi-Step Equations" ] } ## Identify the given dimensions and perimeter Using the *Perimeter of Quadrilaterals* knowledge point $$ \begin{aligned} &\text{Length } (l) = 9a - 10\ &\text{Width } (w) = a + 2\ &\text{Perimeter } (P) = 64 \end{aligned} $$ ## Set up the perimeter equation Using the *Perimeter of Quadrilaterals* knowledge point $$ \begin{aligned} &P = 2(l + w)\ &64 = 2((9a - 10) + (a + 2)) \end{aligned} $$ ## Simplify the algebraic expression Using the *Solving Multi-Step Equations* knowledge point $$ \begin{aligned} &64 = 2(10a - 8)\ &64 = 20a - 16 \end{aligned} $$ ## Solve for the variable a Using the *Solving Multi-Step Equations* knowledge point $$ \begin{aligned} &20a = 80\ &a = 4 \end{aligned} $$ The perimeter of the rectangle is 64. Find a. 4 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Perimeter of Quadrilaterals" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given dimensions and perimeter

Set up the perimeter equation

Simplify the algebraic expression

Solve for the variable a

Answer: