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
![The image presents a mathematical problem involving a right triangle and a square.
- The right triangle has sides labeled as follows:
- One side: \( x \, \text{cm} \)
- Second side: \( (2x + 1) \, \text{cm} \)
- Hypotenuse: \( (3x - 1) \, \text{cm} \)
- The square has each side labeled as:
- \( \left(\frac{1}{2}x + 3\right) \, \text{cm} \)
The task is to find the value of \( x \) when the perimeters of the triangle and the square are equal.
**Solution Approach:**
1. **Calculate the Perimeter of the Triangle:**
\[
\text{Perimeter}_{\triangle} = x + (2x + 1) + (3x - 1)
\]
Simplify to find the total:
2. **Calculate the Perimeter of the Square:**
\[
\text{Perimeter}_{\square} = 4 \times \left(\frac{1}{2}x + 3\right)
\]
Simplify:
3. **Set the Perimeters Equal and Solve for \( x \):**
\[
x + (2x + 1) + (3x - 1) = 4 \times \left(\frac{1}{2}x + 3\right)
\]
Simplify both sides and solve for \( x \).
This approach will yield the value of \( x \) when the two perimeters are equal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed6e2d8f-a94f-4f01-87b0-55d6a3017e4f%2F37f46287-b4ed-4850-acc2-cd5a5be3e8e3%2F7tcx4x8_processed.png&w=3840&q=75)
Transcribed Image Text:The image presents a mathematical problem involving a right triangle and a square.
- The right triangle has sides labeled as follows:
- One side: \( x \, \text{cm} \)
- Second side: \( (2x + 1) \, \text{cm} \)
- Hypotenuse: \( (3x - 1) \, \text{cm} \)
- The square has each side labeled as:
- \( \left(\frac{1}{2}x + 3\right) \, \text{cm} \)
The task is to find the value of \( x \) when the perimeters of the triangle and the square are equal.
**Solution Approach:**
1. **Calculate the Perimeter of the Triangle:**
\[
\text{Perimeter}_{\triangle} = x + (2x + 1) + (3x - 1)
\]
Simplify to find the total:
2. **Calculate the Perimeter of the Square:**
\[
\text{Perimeter}_{\square} = 4 \times \left(\frac{1}{2}x + 3\right)
\]
Simplify:
3. **Set the Perimeters Equal and Solve for \( x \):**
\[
x + (2x + 1) + (3x - 1) = 4 \times \left(\frac{1}{2}x + 3\right)
\]
Simplify both sides and solve for \( x \).
This approach will yield the value of \( x \) when the two perimeters are equal.
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