Please help!

Question

A rancher has 600 feet of fencing to enclose two adjacent rectangular corrals.

(a) Write the area A of the corrals as a function of x.
A(x) =



(b) Create a table showing possible values of and the corresponding areas of the corral. (Round your answers to two decimal places.)
x A
55 ____

60 ____


65 ____



70 ____


75 ____



80 ____



Use the table to estimate the dimensions that will produce the maximum enclosed area. (Round your answers to two decimal places.)
x = ___ft (smaller value)
y = ___ft (larger value)

(c) Use a graphing utility to graph the area function. Use the graph to approximate the dimensions that will produce the maximum enclosed area. (Round your answers to two decimal places.)
x =___ ft (smaller value)
y =____ft (larger value)

(d) Write the area function in standard form to find analytically the dimensions that will produce the maximum area.
A(x) =

Answer 1

Draw two rectangles with a side in common.  Let the length of the common side be x and let y be the length of the figure perpendicular to the common side.  The figure has 3 sides of length x and 2 sides of length y.  

 

So, 3x + 2y = 600

 

             2y = 600 - 3x

 

               y = 300 - 1.5x

 

Area = xy = x(300 - 1.5x)

 

A(x) = x(300 - 1.5x), 0 < x < 200

 

The graph of the area function is a parabola opening downward.  The maximum occurs halfway between the x-intercepts (0 and 200).  

 

So, the maximum area = A(100) = 100(150) = 15,000 ft²

 

 

Answer 2

I don't understand what the value of x represents. Is it the length or width of the rectangle. Probably the essence of the problem relates to the fact that the two rectangles share a side so that the normal definition for the perimeter does not apply.