Find the dimensions of a rectangular rug whose perimeter is 26 ft and whose area is 42 ft². The rug has a length (longer side) of and a width (shorter side) of
Find the dimensions of a rectangular rug whose perimeter is 26 ft and whose area is 42 ft². The rug has a length (longer side) of and a width (shorter side) of
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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Question
![**Problem Statement:**
Find the dimensions of a rectangular rug whose perimeter is 26 ft and whose area is 42 ft².
**Solution Format:**
The rug has a length (longer side) of [ ] and a width (shorter side) of [ ].
**Explanation:**
To solve this problem, we need to use the formulas for the perimeter and area of a rectangle:
1. **Perimeter of a rectangle:** \( P = 2(l + w) \)
2. **Area of a rectangle:** \( A = lw \)
Where \( l \) is the length and \( w \) is the width of the rectangle.
**Steps:**
1. Substitute the given perimeter into the perimeter formula:
\[
2(l + w) = 26
\]
Simplify to:
\[
l + w = 13 \quad \text{(Equation 1)}
\]
2. Substitute the given area into the area formula:
\[
lw = 42 \quad \text{(Equation 2)}
\]
3. Solve Equations 1 and 2 simultaneously to find the values of \( l \) and \( w \).
Note that the boxes provided in the image are placeholders for the numerical solutions to the problem, typically filled in after solving the equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5fc2a9a5-d400-400e-9ea4-34fd53d62fa7%2F1e710c09-1892-4d90-8aeb-52d49f0fc5af%2Fcrvlwjk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the dimensions of a rectangular rug whose perimeter is 26 ft and whose area is 42 ft².
**Solution Format:**
The rug has a length (longer side) of [ ] and a width (shorter side) of [ ].
**Explanation:**
To solve this problem, we need to use the formulas for the perimeter and area of a rectangle:
1. **Perimeter of a rectangle:** \( P = 2(l + w) \)
2. **Area of a rectangle:** \( A = lw \)
Where \( l \) is the length and \( w \) is the width of the rectangle.
**Steps:**
1. Substitute the given perimeter into the perimeter formula:
\[
2(l + w) = 26
\]
Simplify to:
\[
l + w = 13 \quad \text{(Equation 1)}
\]
2. Substitute the given area into the area formula:
\[
lw = 42 \quad \text{(Equation 2)}
\]
3. Solve Equations 1 and 2 simultaneously to find the values of \( l \) and \( w \).
Note that the boxes provided in the image are placeholders for the numerical solutions to the problem, typically filled in after solving the equations.
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