Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![**Understanding the Perimeter of a Rectangle**
The problem displays a rectangle with its dimensions labeled in terms of variables:
- The length of the rectangle is denoted as \(2x\).
- The width of the rectangle is denoted as \(3x + 3\).
**Problem Statement:**
The perimeter of the rectangle is given as 146 units. The task is to determine the length of the longer side of the rectangle from the following options:
- 14 units
- 28 units
- 33 units
- 45 units
**Explanation:**
1. The formula for the perimeter \(P\) of a rectangle is given by:
\[
P = 2 \times (\text{length} + \text{width})
\]
2. Plug in the given dimensions and perimeter:
\[
146 = 2 \times (2x + 3x + 3)
\]
3. Simplify within the parentheses:
\[
146 = 2 \times (5x + 3)
\]
4. Distribute the 2:
\[
146 = 10x + 6
\]
5. Solve for \(x\):
- Subtract 6 from both sides:
\[
140 = 10x
\]
- Divide both sides by 10:
\[
x = 14
\]
6. Determine the length of the longer side:
- The width \(3x + 3\):
\[
3(14) + 3 = 42 + 3 = 45 \, \text{units}
\]
- The length \(2x\):
\[
2(14) = 28 \, \text{units}
\]
Based on these calculations, the longer side of the rectangle is:
**45 units**
**Answer:**
The length of the longer side is 45 units, therefore the correct option is:
(D) 45 units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1fefc4e4-0fc1-4d3a-92e0-1dd9cbc9acda%2Fdcfcf072-8c2c-4df5-a7f4-5af697f0e098%2F5kcrf6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding the Perimeter of a Rectangle**
The problem displays a rectangle with its dimensions labeled in terms of variables:
- The length of the rectangle is denoted as \(2x\).
- The width of the rectangle is denoted as \(3x + 3\).
**Problem Statement:**
The perimeter of the rectangle is given as 146 units. The task is to determine the length of the longer side of the rectangle from the following options:
- 14 units
- 28 units
- 33 units
- 45 units
**Explanation:**
1. The formula for the perimeter \(P\) of a rectangle is given by:
\[
P = 2 \times (\text{length} + \text{width})
\]
2. Plug in the given dimensions and perimeter:
\[
146 = 2 \times (2x + 3x + 3)
\]
3. Simplify within the parentheses:
\[
146 = 2 \times (5x + 3)
\]
4. Distribute the 2:
\[
146 = 10x + 6
\]
5. Solve for \(x\):
- Subtract 6 from both sides:
\[
140 = 10x
\]
- Divide both sides by 10:
\[
x = 14
\]
6. Determine the length of the longer side:
- The width \(3x + 3\):
\[
3(14) + 3 = 42 + 3 = 45 \, \text{units}
\]
- The length \(2x\):
\[
2(14) = 28 \, \text{units}
\]
Based on these calculations, the longer side of the rectangle is:
**45 units**
**Answer:**
The length of the longer side is 45 units, therefore the correct option is:
(D) 45 units.
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