the length of a rectangle is five more than triple the width. if the perimeter is 138 inches, find the dimensions.

the width is inches.
the length is inches.

Question

the length of a rectangle is five more than triple the width. if the perimeter is 138 inches, find the dimensions.

the width is   inches.
the length is   inches.

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", "Perimeter of a Rectangle" ] } ## Translate the word problem into algebraic equations $$ \begin{aligned} &w = \text{width of the rectangle} \ &l = 3w + 5 \ &P = 2(l + w) = 138 \end{aligned} $$ ## Substitute the length expression into the perimeter formula $$ \begin{aligned} 2((3w + 5) + w) &= 138 \ 2(4w + 5) &= 138 \ 8w + 10 &= 138 \end{aligned} $$ ## Solve for width and length $$ \begin{aligned} 8w &= 128 \ w &= 16 \ l &= 3(16) + 5 = 53 \end{aligned} $$ The length of a rectangle is five more than triple the width. If the perimeter is 138 inches, find the dimensions. The width is 16 inches. The length is 53 inches. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Linear Word Problems" ] }

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QUESTION IMAGE

Question

Explanation:

Translate the word problem into algebraic equations

Substitute the length expression into the perimeter formula

Solve for width and length

Answer: