2. a rectangle has a length that is 5 cm more than its width. its perimeter is 38 cm. find the width and the length.

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Linear Equations", "Perimeter Word Problems" ], "current_concepts": [ "Linear Equations", "Perimeter Word Problems" ] } ## Define variables and perimeter formula $$ \begin{aligned} w &= \text{width of the rectangle (in cm)} \ L &= w + 5 \ P &= 2(L + w) = 38 \end{aligned} $$ ## Set up and simplify the equation $$ \begin{aligned} 2((w + 5) + w) &= 38 \ 2(2w + 5) &= 38 \ 2w + 5 &= 19 \ 2w &= 14 \ w &= 7 \end{aligned} $$ ## Calculate the length $$ \begin{aligned} L &= w + 5 \ L &= 7 + 5 \ L &= 12 \end{aligned} $$ Width: $7\text{ cm}$, Length: $12\text{ cm}$ { "subject": "Mathematics", "question_type": "Word Problem", "knowledge_point": [ "Mathematics", "Algebra", "Linear Equations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Define variables and perimeter formula

Set up and simplify the equation

Calculate the length

Answer: