I have a diagram that has 4 rectangular corrals joined together and a barn above it. Fencing is not needed along the back wall of the barn. The perimeter is 200 ft and the question asks...

If each corral is 16 ft. long (front to back) how wide will each corral be and what will be the area of each corral, and the combined area of the 4 corrals?

I got the answers 21 ft for each corral width, 336 ft^2 for the area of each corral and 1,344 ft^2 for the combined area of 4 corrals. Please correct me If I am wrong.

To solve this problem, you need to consider the information provided and determine the dimensions of each corral and the combined area of the four corrals. Let's break down the problem step by step.

We are given that the perimeter of the entire diagram is 200 ft. Since the corrals are rectangular, we can assume that their lengths are 16 ft. We are asked to find the width of each corral.

The perimeter of a rectangle can be calculated by adding up the lengths of all sides. For each corral, there are two sides with a length of 16 ft. Since the barn forms one of the long sides of the corrals, no fencing is needed along the back wall of the barn.

Let's denote the width of each corral as "w". Taking into account the two 16 ft lengths and the fact that no fencing is needed along the barn, here's how we can set up an equation to find the total perimeter:

2w + 2(16ft) = 200ft

Simplifying the equation gives us:

2w + 32ft = 200ft

Now, solve for w:

2w = 200ft - 32ft
2w = 168ft
w = 168ft/2
w = 84ft/1
w = 84ft

So, each corral will have a width of 84 ft.

Next, let's calculate the area of each corral. The area of a rectangle can be found by multiplying its length by its width. In this case, the length is given as 16 ft and the width is calculated as 84 ft:

Area of each corral = 16ft x 84ft
Area of each corral = 1344ft²

Finally, to find the combined area of the four corrals, multiply the area of each corral by 4:

Combined area of the four corrals = 1344ft² x 4
Combined area of the four corrals = 5376ft²

Therefore, the correct answers are:

- Each corral will be 84 ft wide.
- The area of each corral is 1344 ft².
- The combined area of the four corrals is 5376 ft².