Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.1: Angles
Problem 2E
Related questions
Topic Video
Question
please help
![### Question 19: Geometry Problem
#### Instructions:
DE is a midsegment of triangle ABC. Find the value of \( x \).
#### Diagram:
- The figure shows triangle ABC.
- Points D and E are located on the sides AB and AC respectively, such that DE is parallel to BC and D is the midpoint of AB, and E is the midpoint of AC.
- Segment DE is labeled with a length of 5 units.
- The segment BC is labeled with a length of \( x \) units.
#### Answer Choices:
- 20
- 15
- 10
- 5
#### Detailed Solution:
In the context of triangle ABC, since DE is a midsegment, it is parallel to BC and its length is half the length of BC. This means:
\[ DE = \frac{1}{2}BC \]
Given that the length of DE is 5 units, we can set up the equation:
\[ 5 = \frac{1}{2}x \]
To solve for \( x \):
\[ 5 \times 2 = x \]
\[ x = 10 \]
#### Conclusion:
The value of \( x \) is 10.
#### Correct Answer:
- 10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4bd06414-f1f6-4940-956f-9c39fe649804%2F4f0fb634-83aa-4d05-b91e-e7b95fab3fbb%2Fhw2d52r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 19: Geometry Problem
#### Instructions:
DE is a midsegment of triangle ABC. Find the value of \( x \).
#### Diagram:
- The figure shows triangle ABC.
- Points D and E are located on the sides AB and AC respectively, such that DE is parallel to BC and D is the midpoint of AB, and E is the midpoint of AC.
- Segment DE is labeled with a length of 5 units.
- The segment BC is labeled with a length of \( x \) units.
#### Answer Choices:
- 20
- 15
- 10
- 5
#### Detailed Solution:
In the context of triangle ABC, since DE is a midsegment, it is parallel to BC and its length is half the length of BC. This means:
\[ DE = \frac{1}{2}BC \]
Given that the length of DE is 5 units, we can set up the equation:
\[ 5 = \frac{1}{2}x \]
To solve for \( x \):
\[ 5 \times 2 = x \]
\[ x = 10 \]
#### Conclusion:
The value of \( x \) is 10.
#### Correct Answer:
- 10
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
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning