Answer:
The area function is
 .
.
The domain and range of A is  and
 and ![(0, 253.125 m^2]](https://tex.z-dn.net/?f=%280%2C%20253.125%20m%5E2%5D) .
. 
Step-by-step explanation:
The given length of fencing is  .
.
Let the length and width of each pen be  and
 and  respectively as shown in the figure.
 respectively as shown in the figure.
As there are 3 pens, so, the total area, 

From the figure the total length of fencing is  .
.
Here, for a significant area for the animals,  as well as
 as well as  as
 as  and
 and  are the sides of ben.
 are the sides of ben.
From the given value:


Now, from equation (i)


This is the required area function in the terms of variable  .
.
For the domain of area function, from equation (ii)

 [as y>0]
 [as y>0]
So, the domain of area function is  .
.
For the range of area function:
As  or
 or  , then
, then  [from equation (i)]
 [from equation (i)]

Now, differentiate the area function with respect to  .
 .

Equate  to zero to get the extremum point.
  to zero to get the extremum point.



Check this point by double differentiation

As,   , so, point
, so, point  is corresponding to maxima.
 is corresponding to maxima.
Put this value back to equation (iii) to get the maximum value of area function. We have


Hence, the range of area function is ![(0, 253.125 m^2]](https://tex.z-dn.net/?f=%280%2C%20253.125%20m%5E2%5D) .
.