The length of a rectangle is 2 meters more than 2 times the width. If the area is 12 square meters, find the width and the length.

L = 2 W + 2

L * W = 12

substituting ... W (2 W + 2) = 12 ... W^2 + W - 6 = 0

solve for W , then substitute back to find L

thank you R_scott for the help.

Let's assume the width of the rectangle is "w" meters.

According to the given information, the length of the rectangle is 2 meters more than 2 times the width.
So, the length of the rectangle will be 2w + 2 meters.

The formula for the area of a rectangle is length multiplied by width.
Given that the area is 12 square meters, we can set up the equation:

w(2w + 2) = 12

Expanding the equation, we get:
2w^2 + 2w = 12

Rearranging the equation in quadratic form:
2w^2 + 2w - 12 = 0

Now, let's solve the quadratic equation. We can do this by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring method.

Factoring the quadratic equation:
2w^2 + 6w - 4w - 12 = 0
2w(w + 3) - 4(w + 3) = 0
(2w - 4)(w + 3) = 0

Setting each factor equal to zero gives us:
2w - 4 = 0 or w + 3 = 0

Solving for "w":
2w - 4 = 0
2w = 4
w = 2

w + 3 = 0
w = -3

Since width cannot be negative, we can discard the negative solution.

Therefore, the width of the rectangle is 2 meters.

Substituting this value of width into the equation for length:
Length = 2w + 2
Length = 2(2) + 2
Length = 4 + 2
Length = 6

So, the width of the rectangle is 2 meters and the length is 6 meters.

To solve this problem, we need to use the formula for the area of a rectangle, which is length multiplied by width.

Let's start by defining the variables:
Let's say the width of the rectangle is "w" (in meters).
According to the problem, the length is "2 meters more than 2 times the width," which can be expressed as: 2w + 2.

Next, we have the equation for the area of the rectangle:
Area = Length * Width

Substituting the values into the equation, we have:
12 = (2w + 2) * w

To find the width and length, we need to solve this equation:

Step 1: Multiply the terms inside the parentheses:
12 = 2w^2 + 2w

Step 2: Rearrange the equation to set it equal to zero:
2w^2 + 2w - 12 = 0

Step 3: Divide the entire equation by 2 to simplify:
w^2 + w - 6 = 0

Step 4: We can now solve this quadratic equation by factoring it. Factoring gives us:
(w - 2)(w + 3) = 0

So, either w - 2 = 0 or w + 3 = 0

Step 5: Solve for w:
If w - 2 = 0, then w = 2
If w + 3 = 0, then w = -3

Since width cannot be negative in this context, we disregard the solution w = -3.

Therefore, the width of the rectangle, w, is 2 meters.

To find the length, we can substitute the value of w into the expression for length:
Length = 2w + 2
Length = 2(2) + 2
Length = 4 + 2
Length = 6 meters

So, the width of the rectangle is 2 meters, and the length is 6 meters.