the length of a rectangle is three times longer than its width. the perimeter of the rectangle is 16 feet. if $x$ represents the width of the rectangle in feet, which equation can be used to find its value?

$3x + x = 16$
$(3x)(x) = 16$
$3x + 3x + x + x = 16$
$3x + 3x + x = 16$

Question

the length of a rectangle is three times longer than its width. the perimeter of the rectangle is 16 feet. if \$x\$ represents the width of the rectangle in feet, which equation can be used to find its value?

\$3x + x = 16\$
\$(3x)(x) = 16\$
\$3x + 3x + x + x = 16\$
\$3x + 3x + x = 16\$

$3x + x = 16$
$(3x)(x) = 16$
$3x + 3x + x + x = 16$
$3x + 3x + x = 16$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Equation Formulation" ], "new_concepts": [], "current_concepts": [ "Linear Equation Formulation", "Geometric Modeling" ] } ## Define variables for length and width $$ \begin{aligned} &\text{Width} = x \ &\text{Length} = 3x \end{aligned} $$ ## Formulate the perimeter equation $$ \begin{aligned} &\text{Perimeter} = 2(\text{Length}) + 2(\text{Width}) \ &\text{Perimeter} = 3x + 3x + x + x \ &3x + 3x + x + x = 16 \end{aligned} $$

$3x + x = 16$

$(3x)(x) = 16$

$3x + 3x + x + x = 16$

$3x + 3x + x = 16$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear Equation Formulation" ] }

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QUESTION IMAGE

Question

Explanation:

Define variables for length and width

Formulate the perimeter equation

Answer: