Arancher needs to enclose two adjacent rectangularâ corrals, one for cattle and one for sheep. if the river forms one side of the corrals and 180 yd of fencing isâ available, find the largest total area that can be enclosed.

Let B = breadth makes the three sides of 2 corrals &
Let L = Length parallel to the river,

Here, L + 3B = 180 yd
So, L = 180 - 3B

We know that the area of the rectangle,
A = L × B
   =  (180 - 3B) × B
   = 180 B - 3
 
We know that quadratic equation has symmetry,
So, For maximum area Breadth B = 

Here, a = -3 & b 180

So, B = 
          = 30 yd

So, L = 180 - 3B
         = 180 - 3(30)
         = 180 - 90
         = 90

So, Maximum Area = L × B
                               = 90 × 30
                               = 2700 square yards

Therefore, the correct answer is 2700 square yards.