A horse breeder wants to construct a corral next to a horse barn that is L=20 feet long, using the barn as part of one side of the corral as shown in the figure above. The breeder has 320 feet of fencing available.
If the corral has dimensions x and y, with the barn as a part of side y, then
2x+2y-20 = 320
There are lots of values for x and y that fit that requirement. If y is the long side, then we just need x+y=150, so any value of y between 75 and 150 will work fine, but some of the corrals will be long and thin!
I expect the unseen figure puts further constraints on x and y.
To solve this problem, we need to determine the dimensions of the corral that can be constructed using the given amount of fencing.
Let's analyze the figure provided. The corral consists of three sides, with one side being formed by the barn. We need to find the lengths of the other two sides that can be constructed using the available fencing.
The length of the barn is given as L = 20 feet. Let's call the length of the side opposite to the barn A and the length of the adjacent side B, as shown in the figure.
From the image, we can see that the total fencing used is the sum of the lengths of the barn and the two other sides:
20 + A + B = 320
Since the barn length is given as 20 feet, we can rewrite the equation as:
A + B = 320 - 20 = 300
Now, there is an important piece of information missing: we don't know the relationship between the sides A and B. However, we can assume that the corral is a rectangle, which means A = B.
Substituting A = B into the equation, we have:
2A = 300
A = 150
Therefore, the length of the side opposite to the barn is 150 feet, and the adjacent side also has a length of 150 feet.
In conclusion, the dimensions of the corral that can be constructed using 320 feet of fencing are 150 feet for the side opposite to the barn and 150 feet for the adjacent side.