A rectangular garden has a width of x and a perimeter of 100 feet. Find x such that the area of the garden is maximized.

Question

I need help understanding this math problem and how to solve it

Answer 1

perimeter = 2(length) + 2(width) = 100

 

               So, length + width = 50

 

                                 length = 50 - width = 50-x

 

Area = x(50-x)

 

  The graph of y = x(50-x) is a parabola opening downward with x-intercepts 0 and 50. The maximum area occurs halfway between the x-intercepts.

 

Maximum area when x = 25 

 

Answer 2

x represents the width

100 - x represents the length

 

f(x) = x(100 - x)

 

Convert to vertex form and determine maximum.