A barn has 150 feet of fencing and there are 3 rectangular corrals of identical dimensions along the back wall of the barn. The sides of each corral are attached to the barn and fencing is not needed along the back wall of the barn.
If each corral is 30 ft. long (front to back).
What is the maximum area?
To find the maximum area of the three rectangular corrals, we need to determine the dimensions of each corral.
Let's assume the width of each corral is "w" feet.
Given that each corral is 30 ft. long, the total length of the corrals is 3 * 30 = 90 ft.
We also know that the total amount of fencing available is 150 ft. We can find the total amount of fencing used by adding the perimeter of each corral (2w + 30) multiplied by 3 (since there are three corrals).
So, 3 * (2w + 30) = 150.
Simplifying the equation, we get 6w + 90 = 150.
Next, we can solve for "w" by moving the constants to the right side of the equation: 6w = 150 - 90.
So, 6w = 60.
Dividing both sides by 6 gives us w = 10.
Now that we have the width of each corral, we can find the maximum area of each corral by multiplying the width by the length. Since the length is 30 ft, the area of each corral is 10 ft * 30 ft = 300 ft².
Since there are three corrals, the maximum total area is 3 * 300 = 900 ft².
Therefore, the maximum area of the three rectangular corrals is 900 square feet.