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
![### Triangle Proportionality Problem
**Question:**
What is the value of \( x \)?
Enter your answer in the box.
\[ x = \_\_\_ \]
**Diagram Explanation:**
The given diagram features a triangle with a line segment drawn parallel to one of its sides, creating two similar triangles. The lengths provided are:
- The smaller triangle has sides of 5 cm and 3 cm.
- The larger triangle has a side labeled as "2x + 10" and its corresponding segment parallel to the 40 cm side of the larger triangle.
To solve for \( x \), you can use the properties of similar triangles, which state that the ratios of the corresponding sides of similar triangles are equal.
#### Image Explanation:
There is a right triangle where:
- One of the shorter sides is 5 cm.
- The other shorter side above the line segment inside the triangle is 3 cm.
- The entire bottom side of the larger triangle is 40 cm.
- The longer side of the triangle is \( 2x + 10 \).
To find the value of \( x \), you would set up a proportion and solve for \( x \).
\[
\frac{5}{40} = \frac{3}{2x + 10}
\]
From this equation, multiply across to solve the proportion:
\[
5(2x + 10) = 3 \cdot 40
\]
\[
10x + 50 = 120
\]
\[
10x = 70
\]
\[
x = 7
\]
So, the value of \( x \) is 7.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b717370-ac2a-4449-94d5-6954bef42bac%2Fbbcb6b34-3a9b-46ee-b37b-b09f01044295%2Fi5mq4xb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Triangle Proportionality Problem
**Question:**
What is the value of \( x \)?
Enter your answer in the box.
\[ x = \_\_\_ \]
**Diagram Explanation:**
The given diagram features a triangle with a line segment drawn parallel to one of its sides, creating two similar triangles. The lengths provided are:
- The smaller triangle has sides of 5 cm and 3 cm.
- The larger triangle has a side labeled as "2x + 10" and its corresponding segment parallel to the 40 cm side of the larger triangle.
To solve for \( x \), you can use the properties of similar triangles, which state that the ratios of the corresponding sides of similar triangles are equal.
#### Image Explanation:
There is a right triangle where:
- One of the shorter sides is 5 cm.
- The other shorter side above the line segment inside the triangle is 3 cm.
- The entire bottom side of the larger triangle is 40 cm.
- The longer side of the triangle is \( 2x + 10 \).
To find the value of \( x \), you would set up a proportion and solve for \( x \).
\[
\frac{5}{40} = \frac{3}{2x + 10}
\]
From this equation, multiply across to solve the proportion:
\[
5(2x + 10) = 3 \cdot 40
\]
\[
10x + 50 = 120
\]
\[
10x = 70
\]
\[
x = 7
\]
So, the value of \( x \) is 7.
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 3 steps with 4 images
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