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
Solve for the measure of x. After solving for x solve for the length of side AB.
### Diagram Explanation:
The diagram shows a triangle \( \triangle ABC \) with the following side lengths:
- \( AC = 3x + 1 \)
- \( AB = x + 15 \)
- \( BC \) is not labeled and therefore not relevant to this problem.
The triangle appears to be isosceles with sides \( AC \) and \( AB \) marked equal, which is indicated by the two small green lines on these sides.
### Steps to Solve:
1. **Set the equations equal, since \( AC = AB \):**
\[ 3x + 1 = x + 15 \]
2. **Solve for \( x \):**
\begin{align*}
3x + 1 &= x + 15 \\
3x - x &= 15 - 1 \\
2x &= 14 \\
x &= 7
\end{align*}
3. **Find the length of side \( AB \) by substituting \( x = 7 \) into \( AB = x + 15 \):**
\[ AB = 7 + 15 = 22 \]
### Conclusion:
The value of \( x \) is \( 7 \) and the length of side \( AB \) is \( 22 \).
**Note for students:** You can use the paperclip button below to attach any files relevant to your solution.
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*Student can enter a maximum of 3000 characters*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d0c88f8-9b0e-4a87-ae6c-39dd67e2599b%2Fcb6d2283-d446-44ff-8c46-fafd365fa61c%2Fxy1cgem_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Geometry Problem: Solving for x and Finding the Length of Side AB**
### Problem Statement:
Solve for the measure of \( x \). After solving for \( x \), solve for the length of side \( AB \).
### Diagram Explanation:
The diagram shows a triangle \( \triangle ABC \) with the following side lengths:
- \( AC = 3x + 1 \)
- \( AB = x + 15 \)
- \( BC \) is not labeled and therefore not relevant to this problem.
The triangle appears to be isosceles with sides \( AC \) and \( AB \) marked equal, which is indicated by the two small green lines on these sides.
### Steps to Solve:
1. **Set the equations equal, since \( AC = AB \):**
\[ 3x + 1 = x + 15 \]
2. **Solve for \( x \):**
\begin{align*}
3x + 1 &= x + 15 \\
3x - x &= 15 - 1 \\
2x &= 14 \\
x &= 7
\end{align*}
3. **Find the length of side \( AB \) by substituting \( x = 7 \) into \( AB = x + 15 \):**
\[ AB = 7 + 15 = 22 \]
### Conclusion:
The value of \( x \) is \( 7 \) and the length of side \( AB \) is \( 22 \).
**Note for students:** You can use the paperclip button below to attach any files relevant to your solution.
---
*Student can enter a maximum of 3000 characters*
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