Certainly! Let's work through the steps to find the length of James's rectangular yard in inches, given the perimeter and width of his fenced yard.
1. Identify Given Information:
- Perimeter of the yard, [tex]\(P\)[/tex], is 20 feet.
- Width of the yard, [tex]\(W\)[/tex], is 2 feet.
- Conversion factor: 1 foot = 12 inches.
2. Write the Perimeter Formula:
The formula for the perimeter of a rectangle is:
[tex]\[
P = 2L + 2W
\][/tex]
where [tex]\(L\)[/tex] is the length and [tex]\(W\)[/tex] is the width.
3. Substitute Known Values into the Formula:
[tex]\[
20 = 2L + 2(2)
\][/tex]
4. Simplify the Equation:
[tex]\[
20 = 2L + 4
\][/tex]
5. Isolate the Length (L):
Subtract 4 from both sides of the equation:
[tex]\[
20 - 4 = 2L
\][/tex]
[tex]\[
16 = 2L
\][/tex]
6. Solve for the Length (L):
Divide both sides by 2:
[tex]\[
L = \frac{16}{2} = 8 \text{ feet}
\][/tex]
7. Convert the Length to Inches:
Since 1 foot is equal to 12 inches,
[tex]\[
L = 8 \text{ feet} \times 12 \text{ inches/foot} = 96 \text{ inches}
\][/tex]
Therefore, the length of James's rectangular yard in inches is [tex]\( \boxed{96 \text{ inches}} \)[/tex].
