the length of a lacrosse field is 10 yards less than twice its width and the perimeter is 400 yards. the defensive area of the field is $\frac{3}{25}$ of the total field area. find the defensive area of the lacrosse field.

the defensive area of the lacrosse field is
(simplify your answer.)

Question

the length of a lacrosse field is 10 yards less than twice its width and the perimeter is 400 yards. the defensive area of the field is \$\frac{3}{25}\$ of the total field area. find the defensive area of the lacrosse field.

the defensive area of the lacrosse field is
(simplify your answer.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Equations", "Linear Modeling" ], "new_concepts": [ "Geometric Word Problems", "Area Calculations" ], "current_concepts": [ "Linear Equations", "Linear Modeling", "Geometric Word Problems", "Area Calculations" ] } ## Set up equations for dimensions $$ \begin{aligned} &w = \text{width of the field} \ &l = 2w - 10 \ &P = 2(l + w) = 400 \ &2(2w - 10 + w) = 400 \ &3w - 10 = 200 \ &3w = 210 \ &w = 70 \ &l = 2(70) - 10 = 130 \end{aligned} $$ ## Calculate total area $$ \begin{aligned} &A_{\text{total}} = l \times w \ &A_{\text{total}} = 130 \times 70 = 9100 \text{ square yards} \end{aligned} $$ ## Calculate defensive area $$ \begin{aligned} &A_{\text{defensive}} = \frac{3}{25} \times A_{\text{total}} \ &A_{\text{defensive}} = \frac{3}{25} \times 9100 = 3 \times 364 = 1092 \text{ square yards} \end{aligned} $$ The defensive area of the lacrosse field is 1092 square yards. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Linear Modeling" ] }

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Question

Explanation:

Set up equations for dimensions

Calculate total area

Calculate defensive area

Answer: