Sammie bought just enough fencing to border either a rectangular plot or a square plot. The perimeter is of the plots are the same. How many meters of fencing did she buy?

On the square I know all 4 sides are the same. so I would have 4(x+2)as an equation

On the rectangle I know that the length is the same and the width is the same. I know I would use 2(3x+2) and 2(x-1).

I know to use these because I was given a diagram with the x+2 for the square and the 3x+2 and x-1 for the rectangle.

Thats as far as I understand. I don't understand how to set these all up together to work the problem from there.

just set the two expressions equal to each other:

4(x+2) = 2(3x+2) + 2(x-1)

Now you can solve for x and then evaluate either expression for the perimeter.

To solve the problem, we need to equate the perimeters of the square and the rectangle.

For the square, the perimeter is represented by 4 * (x + 2), where x is the length of each side (since all sides of a square are equal).

For the rectangle, the perimeter is represented by 2 * (3x + 2) + 2 * (x - 1), where 3x + 2 represents the length and x - 1 represents the width.

Since the perimeters are equal, we can set up the equation:

4 * (x + 2) = 2 * (3x + 2) + 2 * (x - 1)

Now we can solve for x:

4x + 8 = 6x + 4 + 2x - 2

Simplifying the equation:

4x + 8 = 8x + 2

Rearranging the equation:

8 - 2 = 8x - 4x

6 = 4x

Dividing both sides by 4:

6/4 = x

Simplifying:

3/2 = x

So, each side of the square (x) is equal to 3/2.

To find the total amount of fencing Sammie bought, we can substitute the value of x into either the square or rectangle perimeter equation. Let's choose the square:

Perimeter of the square = 4 * (x + 2) = 4 * (3/2 + 2) = 4 * (3/2 + 4/2) = 4 * (7/2) = 28/2 = 14 meters

Therefore, Sammie bought 14 meters of fencing.

To solve this problem, let's first assign variables to the dimensions of the plots.

Let's say the side length of the square plot is 'x', and the length and width of the rectangular plot are both 'l' and 'w', respectively.

The perimeter of the square plot is simply the sum of all four sides, which would be 4x.

For the rectangular plot, we have the formula for the perimeter: P = 2l + 2w. Given that the length is (3x + 2) and the width is (x - 1), we can substitute these values into the formula to get 2(3x + 2) + 2(x - 1). Simplifying this expression gives us 6x + 4 + 2x - 2.

Since we know that Sammie bought just enough fencing to border either plot, the perimeters of both plots must be equal. So we can now set up the equation:

4x = 6x + 4 + 2x - 2

Now, let's solve for x. Move the variables to one side of the equation and the constants to the other side:

4x - 6x - 2x = 4 - 2

Combine like terms:

-4x = 2

Divide both sides by -4:

x = -2/4
x = -1/2

However, since we are dealing with lengths of a plot, the solution must be a positive number. Thus, we discard the negative solution and consider x = 1/2.

Now that we have the value of x, we can substitute it into any of the perimeter formulas to find the total amount of fencing Sammie bought.

Using the formula for the square, the length of each side would be x + 2, so the perimeter of the square would be 4(x + 2). Plugging in x = 1/2:

Perimeter = 4(1/2 + 2)
Perimeter = 4(5/2)
Perimeter = 10

Therefore, Sammie bought 10 meters of fencing.