a farmer has 800 yards of fencing to enclose a rectangular pasture. Since one side of the pasture boarders a river that side does not need to be fenced. if the side perpendicular to the river must be twice as long as the side parallel to the river, what are the dimensions of the pasture.

Let x = the side parallel to river

then
2x = the two sides perpendicular to the river

x + 2(2x) = 800

x + 4x = 800

5x = 800
5x/5 = 800/5

x = 160
2x = 2(160) =320

320 yard by 160 yard

Why did the farmer bring his fencing skills to the river? Because he wanted to make a splash with his rectangular pasture!

Let's solve the problem step by step. We know that the side that is parallel to the river doesn't need fencing, so we'll ignore that side for now.

Let's assume the side parallel to the river is 'x' yards long. Since the side perpendicular to the river needs to be twice as long, it would be '2x' yards.

Now, we can calculate the total length of fencing needed.

We have 2 sides that are 'x' yards long, which makes a total of '2x' yards of fencing.

And we have 2 sides that are '2x' yards long, which makes a total of '4x' yards of fencing.

Adding all the sides together, we get a total of '2x + 4x = 6x' yards of fencing.

Since the farmer has 800 yards of fencing, we can set up the equation: 6x = 800.

Dividing both sides by 6, we get x = 800/6 = 133.33.

So, the side parallel to the river is approximately 133.33 yards long, and the side perpendicular to the river is twice as long, or approximately 266.67 yards long.

Therefore, the dimensions of the pasture are approximately 133.33 yards by 266.67 yards.

Let's assume that the side perpendicular to the river is x yards long, and the side parallel to the river is y yards long.

Given that the side parallel to the river does not need to be fenced, the perimeter of the pasture can be calculated as follows:

Perimeter = x + y + x (since there are two sides of length x)

We know that the farmer has 800 yards of fencing, so we can set up the equation:

x + y + x = 800

Simplifying the equation, we get:

2x + y = 800

Now, we are also given that the side perpendicular to the river must be twice as long as the side parallel to the river. So, we can write:

x = 2y

Substituting the value of x in terms of y in the equation 2x + y = 800, we get:

2(2y) + y = 800

Simplifying further, we have:

4y + y = 800

5y = 800

Dividing both sides by 5, we get:

y = 800 / 5 = 160

Now, we can find the value of x by substituting the value of y in the equation x = 2y:

x = 2(160) = 320

So, the dimensions of the pasture are 160 yards by 320 yards.

To find the dimensions of the rectangular pasture, we'll break down the problem step by step:

Let's assume the side parallel to the river has a length of 'x' yards.
Since the side perpendicular to the river must be twice as long, it would have a length of '2x' yards.

Now, let's calculate the total length of the three sides that need to be fenced:
- The side parallel to the river: x yards
- The side perpendicular to the river: 2x yards
- The remaining side opposite to the river: x yards

The total length of these three sides is:
x + 2x + x = 4x yards

Now, according to the problem statement, the farmer has 800 yards of fencing. So, we'll set up an equation:

4x = 800

To find the value of 'x', we'll divide both sides of the equation by 4:
4x/4 = 800/4
x = 200

Now we know that 'x' is 200, and the side perpendicular to the river is twice as long, so it would be 2x:
2 * 200 = 400

Therefore, the dimensions of the pasture are 200 yards by 400 yards.