Answer:
The corral is 250 ft by 62.5 ft.
The area of each pen is 5208.3 ft².
Step-by-step explanation:
Let x = length along barn.
Let y = width, and also length of the partitions.
x + 4y = 500
x = 500 - 4y
A = xy
A = (500 - 4y)y
A = 500y - 4y²
dA/dy = 500 - 8y
500 - 8y = 0
8y = 500
y = 62.5
x = 500 - 4y
x = 500 - 4(62.5)
x = 500 - 250
x = 250
The corral is 250 ft by 62.5 ft.
Area of each pen:
x/3 × y = 250 ft / 3 × 62.5 ft =
= 5208.3 ft²
The area of each pen is 5208.3 ft²
