Math Problem Statement
Emma plans to put a fence around her rectangular garden. She has 150 meters of fencing material to make the fence. If there is to be 10 meter opening left for the entrance on one side of the garden, what dimensions should be the graden be for maximum area?
Solution
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Optimization
Formulas
Perimeter equation: x + 2y = 140
Area function: A = x * y
Quadratic equation: A(y) = -2y^2 + 140y
Theorems
Optimization using derivatives
Quadratic formula
Suitable Grade Level
Grades 9-11
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