To solve the given problem, let's break it down step-by-step.
### Step 1: Define the variables
- Let the width of the rectangle be [tex]\( w \)[/tex].
- The length of the rectangle can then be expressed as [tex]\( l = 2w + 3 \)[/tex] (since the length is 3 inches more than twice the width).
### Step 2: Understand the perimeter formula
The perimeter [tex]\( P \)[/tex] of a rectangle is given by the formula:
[tex]\[ P = 2 \times (l + w) \][/tex]
In this problem, we are given that the perimeter [tex]\( P \)[/tex] is 36 inches:
[tex]\[ 2 \times (l + w) = 36 \][/tex]
### Step 3: Substitute the expression for the length [tex]\( l \)[/tex]
From Step 1, we have the relationship [tex]\( l = 2w + 3 \)[/tex]. Substitute this into the perimeter formula:
[tex]\[ 2 \times ((2w + 3) + w) = 36 \][/tex]
### Step 4: Simplify the equation
Combine the terms inside the parentheses:
[tex]\[ 2 \times (3w + 3) = 36 \][/tex]
### Step 5: Distribute the 2
[tex]\[ 6w + 6 = 36 \][/tex]
### Step 6: Solve for [tex]\( w \)[/tex]
First, isolate the term with [tex]\( w \)[/tex]:
[tex]\[ 6w + 6 - 6 = 36 - 6 \][/tex]
[tex]\[ 6w = 30 \][/tex]
Now, divide both sides by 6:
[tex]\[ w = \frac{30}{6} \][/tex]
[tex]\[ w = 5 \][/tex]
### Step 7: Find the length [tex]\( l \)[/tex]
Using the width [tex]\( w = 5 \)[/tex] inches, substitute back into the expression for the length:
[tex]\[ l = 2w + 3 \][/tex]
[tex]\[ l = 2 \times 5 + 3 \][/tex]
[tex]\[ l = 10 + 3 \][/tex]
[tex]\[ l = 13 \][/tex]
### Conclusion
The width of the rectangle is 5 inches, and the length is 13 inches.
Thus, the dimensions of the rectangle are:
- Width: 5 inches
- Length: 13 inches
