SOLUTION: Suppose you had 140 feet of fence to make a rectangular garden. What are possible dimensions of the garden? What length and width would give you the maximum area? I know you

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Suppose you had 140 feet of fence to make a rectangular garden. What are possible dimensions of the garden? What length and width would give you the maximum area? I know you      Log On


   

Question 843378: Suppose you had 140 feet of fence to make a rectangular garden. What are possible dimensions of the garden? What length and width would give you the maximum area?


I know you use the 2L+2W=140
L+W=70, but how do I find the length and width that would give me the maximum area?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The maximum area occurs when the rectangular garden is a square of side length 35 ft. To prove this, note that A = LW = L(70-L), the vertex of the parabola occurs at L = 35 ft. Can also be proven via AM-GM inequality or calculus.