Math Problem Statement
A track and field playing area is in the shape of a rectangle with semicircles at each end. See the figure. The inside perimeter of the track is to be 1300 meters. What should the dimensions of the rectangle be so that the area of the rectangle is maximized? Question content area bottom Part 1 The dimensions of the rectangle are
enter your response here meters. (Use a comma to separate answers as needed. Type an integer or decimal rounded to the nearest hundredth as needed.)
Solution
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Math Problem Analysis
Mathematical Concepts
Geometry
Optimization
Differential Calculus
Formulas
Perimeter formula: 2L + πW = 1300
Area of the rectangle: A = L × W
Maximizing area: dA/dW = 0
Theorems
Optimization through differentiation
First derivative test
Suitable Grade Level
Grades 10-12
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