Answer:
Corral dimensions:
x = 50 ft
y = 33,33 ft
A(max) = 1666,5 ft²
A(pen) = 833,25 ft²
Step-by-step explanation:
Let´s call "x" and "y" dimensions of the corral
Then the perimeter is:
p = 2*x + 2*y , and in order to get two pens of equal dimensions we need to split by the use of other length y then
p = 2*x + 3*y = 200
y = (200 - 2*x)/3
Area of the corral
A(c) = x*y
Area as function of x is:
A(x) = x * ( 200 - 2*x)/3
A(x) = (200*x - 2*x²)/3
A(x) = (200/3)*x - (2/3)*x²
Taking derivatives on both sides of the equation:
A´(x) = 200/3 - (4/3)*x
A´(x) = 0 200/3 - (4/3)*x = 0 ⇒ 200 - 4*x = 0
x = 50 ft.
y = ( 200 - 100)/3
y = 100/3
y = 33,33 ft
A(max) = 33,33*50
A(max) = 1666,5 ft²
Area of each pen
A₂ = 833,25 ft²
