Math Problem Statement

Find the dimensions of the rectangular corral producing the greatest enclosed area given 200 feet of fencing.

Solution

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Math Problem Analysis

Mathematical Concepts

Optimization
Quadratic Functions
Derivatives

Formulas

Perimeter of a rectangle: P = 2L + 2W
Area of a rectangle: A = L × W
Derivative of the area function: dA/dL = 100 - 2L

Theorems

Quadratic Optimization Theorem: The maximum or minimum of a quadratic function occurs at its vertex.

Suitable Grade Level

Grades 10-12