A rectangle has a length that is three feet more than twice it’s width. What would the perimeter of this rectangle be if the width was 10 feet?

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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A rectangle has a length that is three feet more than twice it’s width. What would the perimeter of this rectangle be if the width was 10 feet?
### Transcript for Educational Website

(b) What would the perimeter of this rectangle be if the width was 10 feet?

Below this question, there is some handwritten work and calculations, which include:

- A crossed-out calculation or mark that is difficult to decipher.
- Handwritten “3” on the left margin.
- Another calculation with a series of numbers that seem to be erased but include fragments like “51” and “9.94”.
- Steps for adding numbers, as shown by "10 + 60" which totals to "78".

### Explanation of Handwritten Calculations

These markings appear to be work-in-progress calculations related to solving the problem. Here's a likely breakdown of the steps:

1. **Perimeter Calculation:**
   - The formula for the perimeter (\(P\)) of a rectangle is given by:
     \[
     P = 2 \times (\text{length} + \text{width})
     \]
   - Given width (\(w\)) is 10 feet, calculations are done to find length (\(l\)).

2. **Using the Provided Information**:
   - There is an indication that the total perimeter is possibly 78 feet (shown at the bottom: "10 + 60 = 78").

The provided calculations seem to verify the length if the perimeter is correctly calculated using the given width.

### Simplified Explanation for Students

1. **Find the Length Given Width and Perimeter:**
   - If width \(w = 10\) feet and perimeter \(P = 78\) feet, use the formula:
     \[
     P = 2 \times (\text{length} + 10) = 78
     \]
   - Solving, we get:
     \[
     2 \times (\text{length} + 10) = 78 
     \]
     \[
     \text{length} + 10 = 39 
     \] 
     \[
     \text{length} = 29 \, \text{feet}
     \]

2. **Verify Perimeter Calculation:**
   - Plugging values back:
     \[
     P = 2 \times (29 + 10) = 2 \times 39 = 78 \text{ feet}
     \]
   - This confirms the calculation.

Students should ensure they understand each step and verify parts of their calculations by substitution.
Transcribed Image Text:### Transcript for Educational Website (b) What would the perimeter of this rectangle be if the width was 10 feet? Below this question, there is some handwritten work and calculations, which include: - A crossed-out calculation or mark that is difficult to decipher. - Handwritten “3” on the left margin. - Another calculation with a series of numbers that seem to be erased but include fragments like “51” and “9.94”. - Steps for adding numbers, as shown by "10 + 60" which totals to "78". ### Explanation of Handwritten Calculations These markings appear to be work-in-progress calculations related to solving the problem. Here's a likely breakdown of the steps: 1. **Perimeter Calculation:** - The formula for the perimeter (\(P\)) of a rectangle is given by: \[ P = 2 \times (\text{length} + \text{width}) \] - Given width (\(w\)) is 10 feet, calculations are done to find length (\(l\)). 2. **Using the Provided Information**: - There is an indication that the total perimeter is possibly 78 feet (shown at the bottom: "10 + 60 = 78"). The provided calculations seem to verify the length if the perimeter is correctly calculated using the given width. ### Simplified Explanation for Students 1. **Find the Length Given Width and Perimeter:** - If width \(w = 10\) feet and perimeter \(P = 78\) feet, use the formula: \[ P = 2 \times (\text{length} + 10) = 78 \] - Solving, we get: \[ 2 \times (\text{length} + 10) = 78 \] \[ \text{length} + 10 = 39 \] \[ \text{length} = 29 \, \text{feet} \] 2. **Verify Perimeter Calculation:** - Plugging values back: \[ P = 2 \times (29 + 10) = 2 \times 39 = 78 \text{ feet} \] - This confirms the calculation. Students should ensure they understand each step and verify parts of their calculations by substitution.
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