The points T, U, V and W all lie on the same line segment, in that order, such that the ratio of TU : UV : VW is equal to 1 : 5 : 2. If TW = 32, findUW.
The points T, U, V and W all lie on the same line segment, in that order, such that the ratio of TU : UV : VW is equal to 1 : 5 : 2. If TW = 32, findUW.
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
![### Educational Transcript
**Problem:**
The points \( T \), \( U \), \( V \), and \( W \) all lie on the same line segment, in that order, such that the ratio of \( TU : UV : VW \) is equal to \( 1 : 5 : 2 \). If \( TW = 32 \), find \( UW \).
**Solution Explanation:**
To solve this problem, observe the given ratio \( TU : UV : VW = 1 : 5 : 2 \). Let the lengths be represented as:
- \( TU = x \)
- \( UV = 5x \)
- \( VW = 2x \)
Since \( TW \) is the total length from point \( T \) to point \( W \), we have:
\[ TW = TU + UV + VW \]
Substitute the lengths in terms of \( x \):
\[ TW = x + 5x + 2x \]
Combine the terms to simplify:
\[ TW = 8x \]
We know from the problem statement that \( TW = 32 \). Set up the equation:
\[ 8x = 32 \]
Solve for \( x \):
\[ x = \frac{32}{8} \]
\[ x = 4 \]
Now we need to find \( UW \):
\[ UW = UV + VW = 5x + 2x = 7x \]
Substitute \( x \) with 4:
\[ UW = 7 \times 4 = 28 \]
So, \( UW \) is 28 units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e1bdb0e-93e0-4643-a548-ab4acb8278f7%2F7cda7a68-a78f-4b22-917c-4b06f4357527%2Fc7eefxn_processed.png&w=3840&q=75)
Transcribed Image Text:### Educational Transcript
**Problem:**
The points \( T \), \( U \), \( V \), and \( W \) all lie on the same line segment, in that order, such that the ratio of \( TU : UV : VW \) is equal to \( 1 : 5 : 2 \). If \( TW = 32 \), find \( UW \).
**Solution Explanation:**
To solve this problem, observe the given ratio \( TU : UV : VW = 1 : 5 : 2 \). Let the lengths be represented as:
- \( TU = x \)
- \( UV = 5x \)
- \( VW = 2x \)
Since \( TW \) is the total length from point \( T \) to point \( W \), we have:
\[ TW = TU + UV + VW \]
Substitute the lengths in terms of \( x \):
\[ TW = x + 5x + 2x \]
Combine the terms to simplify:
\[ TW = 8x \]
We know from the problem statement that \( TW = 32 \). Set up the equation:
\[ 8x = 32 \]
Solve for \( x \):
\[ x = \frac{32}{8} \]
\[ x = 4 \]
Now we need to find \( UW \):
\[ UW = UV + VW = 5x + 2x = 7x \]
Substitute \( x \) with 4:
\[ UW = 7 \times 4 = 28 \]
So, \( UW \) is 28 units.
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 with 2 images
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