a rectangular room is 1.9 times as long as it is wide, and its perimeter is 33 meters. find the dimension of the room.

the length is : meters and the width is meters. enter the dimensions as decimals rounded to at least one decimal place.

Question

a rectangular room is 1.9 times as long as it is wide, and its perimeter is 33 meters. find the dimension of the room.

the length is :   meters and the width is   meters. enter the dimensions as decimals rounded to at least one decimal place.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Algebraic Translation", "Linear Word Problems" ], "new_concepts": [], "current_concepts": [ "Algebraic Translation", "Linear Word Problems", "System of Linear Equations" ] } ## Set up the system of equations $$ \begin{aligned} L &= 1.9W \ 2L + 2W &= 33 \end{aligned} $$ ## Substitute and solve for width $$ \begin{aligned} 2(1.9W) + 2W &= 33 \ 3.8W + 2W &= 33 \ 5.8W &= 33 \ W &= \frac{33}{5.8} \approx 5.689655 \end{aligned} $$ ## Calculate the length $$ \begin{aligned} L &= 1.9 \times 5.689655 \approx 10.81034 \ L &\approx 10.8 \ W &\approx 5.7 \end{aligned} $$ A rectangular room is 1.9 times as long as it is wide, and its perimeter is 33 meters. Find the dimension of the room. The length is : 10.8 meters and the width is 5.7 meters. Enter the dimensions as decimals rounded to at least one decimal place. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Linear Word Problems" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the system of equations

Substitute and solve for width

Calculate the length

Answer: