Question

Find the dimensions of the rectangular corral producing the greatest enclosed area given 200 feet of fencing.

Answer 1

Suppose x is the length and y is the width of rectangular corral.

The objective is to determine the largest area of the corral if it has 200 feet of fencing.

 

Apply formula of perimeter of rectangle as follows.

2(x + y) = 200

    x + y = 100

          x = 100 - y …... (1)

 

Now apply area of rectangle as follows.

A = (100 – y)y

A = -y2 + 100y

 

Here width can be determined by finding axis of symmetry.

y = -b/2a

   = -100/-2

   = 50

 

Substitute value of y in (1).

x = 100 – 50

   = 50

Therefore, the length of the rectangular corral is 50 feet and width is also 50 feet.

Therefore, the length of the rectangular corral is 50 feet and width is also 50 feet.