The perimeter of a rectangle is 53 meters. The length is 2.3 meters longer than the width, w. Write and solve an equation to find the width of the rectangle.

Can someone show and explain how to solve this step by step? Trying to get some late math done. v.v

perimeter is two lengths plus two widths ... P = 2 L + 2 W

The length is 2.3 meters longer than the width ... L = W + 2.3
...substitute for the length

53 = 2 (W + 2.3) + 2 W = 4 W + 4.6

solve for W , then substitute back to find L

Step 1:

Let's start by assigning a variable to the width of the rectangle. Let's call it "w."

Step 2:
According to the given information, the length is 2.3 meters longer than the width. Therefore, the length can be expressed as "w + 2.3."

Step 3:
To find the perimeter of a rectangle, we need to add up the lengths of all four sides. In this case, there are two lengths and two widths.

Perimeter = 2(length) + 2(width)

Substituting the expressions for length and width:

Perimeter = 2(w + 2.3) + 2w

Step 4:
We know that the perimeter is given as 53 meters, so we set up the equation:

53 = 2(w + 2.3) + 2w

Step 5:
Let's solve the equation step-by-step.

Start by distributing the 2 to both terms inside the parentheses:

53 = 2w + 4.6 + 2w

Combine like terms:

53 = 4w + 4.6

Step 6:
Next, let's isolate the variable term by subtracting 4.6 from both sides of the equation:

53 - 4.6 = 4w + 4.6 - 4.6

48.4 = 4w

Step 7:
Finally, divide both sides by 4 to solve for the width:

48.4/4 = 4w/4

12.1 = w

Step 8:
So, the width of the rectangle is 12.1 meters.

To summarize, the step-by-step solution for finding the width of the rectangle is as follows:

1. Assign the variable w to the width.
2. Express the length as w + 2.3.
3. Set up the perimeter equation: Perimeter = 2(w + 2.3) + 2w.
4. Substitute the given perimeter value of 53 into the equation.
5. Simplify the equation.
6. Isolate the variable term on one side of the equation.
7. Divide both sides by the coefficient of the variable to solve for w.
8. The width of the rectangle is 12.1 meters.

To find the width of the rectangle, let's first define some variables:

Let w be the width of the rectangle.
The length is 2.3 meters longer than the width, so the length would be w + 2.3.

The perimeter of a rectangle is found by adding all the sides together. In this case, we have two equal lengths (w + 2.3) and two equal widths (w).

The perimeter of a rectangle can be expressed as:

Perimeter = 2 * (Length + Width)

Substituting the values into the equation, we have:

53 = 2 * ((w + 2.3) + w)

Now, let's simplify and solve the equation step by step:

1. Distribute the 2 to the terms inside the parentheses:
53 = 2w + 4.6 + 2w

2. Combine like terms on the right side of the equation:
53 = 4w + 4.6

3. To isolate the variable, subtract 4.6 from both sides of the equation:
53 - 4.6 = 4w

4. Simplify the left side of the equation:
48.4 = 4w

5. Divide both sides of the equation by 4 to solve for w:
w = 48.4 / 4

6. Calculate the result:
w = 12.1

Therefore, the width of the rectangle is 12.1 meters.

4.6?