To solve for the width of a rectangle when given the perimeter and a relationship between the length and width, follow these steps:
1. Understand the given values:
- Perimeter of the rectangle is 38 inches.
- Length of the rectangle is 3 inches more than the width.
2. Define the variables:
- Let the width be [tex]\( w \)[/tex].
- The length will be [tex]\( w + 3 \)[/tex].
3. Use the perimeter formula for a rectangle:
- The formula for the perimeter [tex]\( P \)[/tex] of a rectangle is:
[tex]\[
P = 2 \times (\text{Length} + \text{Width})
\][/tex]
4. Substitute the known values into the formula:
- Given [tex]\( P = 38 \)[/tex], and the length is [tex]\( w + 3 \)[/tex], the formula becomes:
[tex]\[
38 = 2 \times (w + (w + 3))
\][/tex]
5. Simplify the equation:
- First, combine like terms inside the parentheses:
[tex]\[
38 = 2 \times (2w + 3)
\][/tex]
- Next, distribute the 2:
[tex]\[
38 = 4w + 6
\][/tex]
6. Solve for [tex]\( w \)[/tex]:
- Isolate [tex]\( 4w \)[/tex] by subtracting 6 from both sides:
[tex]\[
38 - 6 = 4w
\][/tex]
[tex]\[
32 = 4w
\][/tex]
- Divide both sides by 4:
[tex]\[
w = \frac{32}{4}
\][/tex]
[tex]\[
w = 8
\][/tex]
Thus, the width of the rectangle is 8 inches.
