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 function?
What is the width of each corral?
What is the area of each corral, and the combined area of the four corrals?
Well, this sounds like quite the "corralling" problem! Let's break it down and have some fun finding the answers.
First, let's find the width of each corral. Since the fencing is only needed for the other three sides of each corral, we can subtract the length of the barn fence from the total perimeter of each corral. So, each corral has 2 sides that need fencing, with a combined length of (30 ft + 30 ft + 150 ft) - 150 ft = 60 ft. Since there are two sides, dividing by 2 gives us a width of 30 ft.
Now, let's calculate the area of each corral. The area of a rectangle is found by multiplying its length by its width. In this case, the length is 30 ft and the width is 30 ft, so the area of each corral is 30 ft * 30 ft = 900 sq ft.
Finally, let's find the combined area of the four corrals. Since all the corrals have identical dimensions, we can simply multiply the area of one corral by 4. So, the combined area of the four corrals is 900 sq ft * 4 = 3600 sq ft.
Ta-da! We've corralled all the answers for you. Hope that put a smile on your face, even if it's not a circus in here!
To answer these questions, we need to understand the given information and use some mathematical calculations.
1. Function:
The question does not mention any specific function. It seems like we are trying to find various measurements related to the three rectangular corrals.
2. Width of each corral:
Let's assume the width of each corral is "w" feet.
We know that each corral is 30 ft. long, so the total length of all three corrals (front to back) would be 3 x 30 = 90 ft.
The total amount of fencing used for the three corrals is 150 ft. Since the fencing is only needed along the sides and not along the back wall of the barn, only the width of the corrals contributes to the total fencing. Therefore, the total amount of fencing used can be represented as:
3w = 150
To find the width of each corral, we can divide both sides of the equation by 3:
w = 150 / 3
w = 50
So, the width of each corral is 50 ft.
3. Area of each corral and combined area of the four corrals:
The area of a rectangle can be calculated by multiplying its length and width.
For each corral, the length is given as 30 ft, and we have already determined the width as 50 ft.
Therefore, the area of each corral is:
Area of one corral = length x width = 30 ft x 50 ft = 1500 sq. ft.
Since there are three identical corrals, the combined area of the four corrals would be:
Combined area of four corrals = Area of one corral x 3 = 1500 sq. ft x 3 = 4500 sq. ft.
So, the area of each corral is 1500 sq. ft, and the combined area of the four corrals is 4500 sq. ft.