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
Concept explainers
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
![**Problem Statement**:
In the diagram, \( \triangle JCQ \sim \triangle TYA \). Find the value of \( x \).
**Diagram Details**:
There are two triangles in the diagram:
1. **Triangle JCQ**:
- Side \( JC = 36 \)
- Side \( CQ = 40 \)
- Side \( JQ = 32 \)
2. **Triangle TYA**:
- Side \( TY = x \)
- Side \( YA = 30 \)
- Side \( TA = 24 \)
**Options**:
A multiple-choice list is provided to find the value of \( x \):
- 27
- 26
- 36
- 28
**Explanation**:
Given that \( \triangle JCQ \sim \triangle TYA \), this means that the two triangles are similar and hence, their corresponding sides are proportional. This similarity can be expressed by the proportion of corresponding side lengths:
\[
\frac{JC}{TY} = \frac{JQ}{TA}
\]
Given the side lengths for triangular relationships:
\[
\frac{36}{x} = \frac{32}{24}
\]
Cross-multiplying to solve for \( x \),
\[
36 \times 24 = 32 \times x
\]
\[
864 = 32x
\]
\[
x = \frac{864}{32}
\]
\[
x = 27
\]
Thus the value of \( x \) is 27.
**Answer**: 27](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d44061d-5891-4c6f-9f7e-bc7f6369bc06%2F6008698c-a113-43fc-83d2-682e416c2435%2Fmnvnysj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement**:
In the diagram, \( \triangle JCQ \sim \triangle TYA \). Find the value of \( x \).
**Diagram Details**:
There are two triangles in the diagram:
1. **Triangle JCQ**:
- Side \( JC = 36 \)
- Side \( CQ = 40 \)
- Side \( JQ = 32 \)
2. **Triangle TYA**:
- Side \( TY = x \)
- Side \( YA = 30 \)
- Side \( TA = 24 \)
**Options**:
A multiple-choice list is provided to find the value of \( x \):
- 27
- 26
- 36
- 28
**Explanation**:
Given that \( \triangle JCQ \sim \triangle TYA \), this means that the two triangles are similar and hence, their corresponding sides are proportional. This similarity can be expressed by the proportion of corresponding side lengths:
\[
\frac{JC}{TY} = \frac{JQ}{TA}
\]
Given the side lengths for triangular relationships:
\[
\frac{36}{x} = \frac{32}{24}
\]
Cross-multiplying to solve for \( x \),
\[
36 \times 24 = 32 \times x
\]
\[
864 = 32x
\]
\[
x = \frac{864}{32}
\]
\[
x = 27
\]
Thus the value of \( x \) is 27.
**Answer**: 27
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning