You have 188 feet of fencing to enclose a rectangular region. What is the maximum area?

Question

5634 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-09T00:38:59

#2209# square feet

#1#. Make "let" statements to represent the length and width of the rectangular region.

Let #x# represent the length.
Let #(188-2x)/2=94-x# represent the width.

#2#. Create an algebraic expression represent the area of a rectangle.

#A_"rectangle"=x(94-x)#

#3#. Complete the square.

#A_"rectangle"=94x-x^2#

#A_"rectangle"=-(x^2-94x)#

#A_"rectangle"=-(x^2-94x+(-94/2)^2-(-94/2)^2)#

#A_"rectangle"=-(x-47)^2+2209#

#:.#, the maximum area of the rectangular region is #2209# square feet.