let 'x' and 'y' be the sides of the rectangular corral.

let 'x' be the side the 2 adjacent corrals share.

since the perimeter of 2 corrals together is 296 ft we can write

x + y + y + x + y + y = 296

2x + 4y = 296 divide both sides by 2

x + 2y = 148 => y = 74 - (x/2)

the area of the 2 corrals together is

A = x*(2y) = 2xy

if we replace for y = 74 - (x/2) we get

A = 2x * (74 - (x/2))

A = 148x - x^2

The quadratic function A(x) = 148x - x^2 = -x^2 + 148x + 0 has maximum at its vertex (since the quotient in front of x^2 is negative) that is

A max = 0 - 148^2/ 4*(-1) = 5476 ft^2

and by solving the quadratic

-x^2 + 148x = 5476

-x^2 + 148x - 5476 = 0

we find

x = 74 ft

y = 74 - (x/2)

y = 74 - (74/2)

y = 74 - 37

y = 37 ft

The maximum total area is 5476 ft^2.

The dimensions for the individual corral is 74 ft and 37 ft.