Question
A rectangular field is twelve times as long as it is wide. If the perimeter of the field is 1430 feet, what are the dimensions of the field? The width of the field is The length of the field is Question Help: \( \square \) Message instructor Submit Question
Ask by Chandler Salinas. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The width of the field is 55 feet, and the length is 660 feet.
Solution
To determine the dimensions of the rectangular field, let's follow these steps:
1. **Define Variables:**
- Let \( w \) be the width of the field (in feet).
- Since the length is twelve times the width, the length \( l \) is \( 12w \).
2. **Express the Perimeter:**
- The formula for the perimeter \( P \) of a rectangle is:
\[
P = 2(l + w)
\]
- Given that the perimeter is 1430 feet:
\[
2(l + w) = 1430
\]
3. **Substitute the Length:**
- Replace \( l \) with \( 12w \):
\[
2(12w + w) = 1430
\]
\[
2(13w) = 1430
\]
\[
26w = 1430
\]
4. **Solve for Width (\( w \)):**
\[
w = \frac{1430}{26} = 55 \text{ feet}
\]
5. **Find the Length (\( l \)):**
\[
l = 12w = 12 \times 55 = 660 \text{ feet}
\]
**Final Dimensions:**
- **Width of the field:** 55 feet
- **Length of the field:** 660 feet
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To find the dimensions of the field, let's denote the width as \( w \). The length will then be \( 12w \). The formula for the perimeter \( P \) of a rectangle is given by \( P = 2 \times (\text{length} + \text{width}) \). Plugging in the values: \[ 1430 = 2 \times (12w + w) \] \[ 1430 = 2 \times 13w \] \[ 1430 = 26w \] \[ w = \frac{1430}{26} \] \[ w = 55 \, \text{feet} \] Now, substituting back to find the length: \[ \text{length} = 12w = 12 \times 55 = 660 \, \text{feet} \] So, the dimensions of the field are: The width of the field is 55 feet. The length of the field is 660 feet.
