A rancher has 800 feet of fencing to enclose two adjacent rectangular corrals (see figure)

I FOUND YOUR COMPLETE QUESTION IN OTHER SOURCES.
 PLEASE SEE ATTACHED IMAGE.

 The perimeter is given by:
 P = 2 (2x) + 2 (y)
 Rewriting we have:
 P = 4x + 2y
 Substituting:
 800 = 4x + 2y
 The area is:
 A = 2x * y
 We write the area as a function of x:
 A (x) = 2x * (400-2x)
 Rewriting:
 A (x) = 800x-4x ^ 2
 We derive:
 A '(x) = 800-8x
 We match zero:
 0 = 800-8x
 We clear x:
 x = 800/8
 x = 100 feet
 We check that it is a maximum. For this, we look for the second derivative:
 A '' (x) = - 8
 We evaluate x = 100
 A '' (100) = - 8 <0 (is a maximum)
 We look for the other dimension:
 y = 400-2x
 y = 400-2 (100)
 y = 400-200
 y = 200 feet
 Answer:
 The dimensions that should be used are that the enclosed area will be a maximum are:
 x = 100 feet
 y = 200 feet