you have 350 feet of fencing to enclose a rectangular plot that borders on a river. if you do not fence the side along the river, find the length and width of the plot that will maximize the area. what is the largest area that can be enclosed?

the width, labeled x in the figure, is feet.
(type an integer or decimal.)

Question

you have 350 feet of fencing to enclose a rectangular plot that borders on a river. if you do not fence the side along the river, find the length and width of the plot that will maximize the area. what is the largest area that can be enclosed?

the width, labeled x in the figure, is feet.
(type an integer or decimal.)

the width, labeled x in the figure, is   feet.
(type an integer or decimal.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Quadratic Word Problems", "Maximum Value of Quadratic" ], "new_concepts": [], "current_concepts": [ "Quadratic Word Problems", "Maximum Value of Quadratic", "Vertex Form of a Quadratic" ] } ## Define the area function Using the **Quadratic Word Problems** knowledge point $$ \begin{aligned} &\text{Width} = x\ &\text{Length} = 350 - 2x\ &A(x) = x(350 - 2x) = -2x^2 + 350x \end{aligned} $$ ## Find the vertex to maximize area Using the **Maximum Value of Quadratic** knowledge point $$ \begin{aligned} &x = -\frac{b}{2a} = -\frac{350}{2(-2)} = 87.5 \end{aligned} $$ The width, labeled x in the figure, is 87.5 feet. (Type an integer or decimal.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Word Problems" ] }

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Question

Explanation:

Define the area function

Find the vertex to maximize area

Answer: