a rectangular prism must have a base with an area of no more than 27 square meters. the width of the base must be 9 meters less than the height of the prism. the length of the base must be 6 meters more than the width of the base. find the maximum height of the prism.
let $x$ = the height of the prism
$x - 9$ =
the width of the base
the length of the base
the area of the base

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Algebraic Translation", "Word Problem Analysis" ], "new_concepts": [], "current_concepts": [ "Algebraic Translation", "Word Problem Analysis", "Linear Equation Formulation" ] } ## Translate the height variable to the width of the base $$ \begin{aligned} &\text{Let } x = \text{the height of the prism.}\ &\text{The width of the base is } 9 \text{ meters less than the height of the prism.}\ &\text{Therefore, } x - 9 = \text{the width of the base.} \end{aligned} $$

the width of the base

the length of the base

the area of the base

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Algebraic Translation" ] }

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Question

Explanation:

Translate the height variable to the width of the base

Answer: