Math Problem Statement
Find the dimensions of the rectangular corral producing the greatest enclosed area given 200 feet of fencing.
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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
Related Recommendation
Optimization of a Rectangular Enclosure with 600 Feet of Fencing
Maximizing the Area of Two Adjacent Rectangular Corrals Using Quadratic Optimization
Maximizing Area for Adjacent Rectangular Corrals with 160 Feet of Fencing
Maximizing Area with 2100 Feet of Fencing for Six Corrals
Maximize Area of Rectangular Corral with Creek Side - Problem Solution