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
Topic Video
Question
![---
### Understanding Rectangles and Diagonals in Geometry
#### Problem Statement:
Consider the rectangle TREC with diagonals. We are tasked with finding the length of ET.
#### Diagram:
There is a rectangle labeled TREC with diagonals TR and EC intersecting at point X. The diagonals are given expressions as follows:
- TR is labeled as \(2x - 3\).
- EC is labeled as \(x + 7\).
#### Question:
What is the length of ET?
#### Answer Choices:
1. 10 units
2. 17 units
3. 20 units
4. 34 units
#### Explanation:
To find the length of ET, which is half of the diagonal TR (since in rectangles, diagonals bisect each other), the following steps are involved:
1. **Equate the diagonals**:
Since diagonals of a rectangle are equal:
\[
2x - 3 = x + 7
\]
2. **Solve for x**:
\[
2x - x = 7 + 3
\]
\[
x = 10
\]
3. **Substitute x back into the expressions**:
\[
TR = 2x - 3 = 2(10) - 3 = 20 - 3 = 17 \text{ units}
\]
4. **Calculate ET**:
Since diagonals of a rectangle are equal and each diagonal bisects into two equal parts:
\[
ET = \frac{TR}{2} = \frac{17}{2} = 8.5 \text{ units}
\]
However, it seems there might be a mistake in the choices given. Please check the context of study materials for correct choices. The correct solution based on steps given should be 17 units as the length of TR, not ET.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1fefc4e4-0fc1-4d3a-92e0-1dd9cbc9acda%2F82624fee-e94a-4ca1-be47-65671e968dde%2Fp1ukl59_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Understanding Rectangles and Diagonals in Geometry
#### Problem Statement:
Consider the rectangle TREC with diagonals. We are tasked with finding the length of ET.
#### Diagram:
There is a rectangle labeled TREC with diagonals TR and EC intersecting at point X. The diagonals are given expressions as follows:
- TR is labeled as \(2x - 3\).
- EC is labeled as \(x + 7\).
#### Question:
What is the length of ET?
#### Answer Choices:
1. 10 units
2. 17 units
3. 20 units
4. 34 units
#### Explanation:
To find the length of ET, which is half of the diagonal TR (since in rectangles, diagonals bisect each other), the following steps are involved:
1. **Equate the diagonals**:
Since diagonals of a rectangle are equal:
\[
2x - 3 = x + 7
\]
2. **Solve for x**:
\[
2x - x = 7 + 3
\]
\[
x = 10
\]
3. **Substitute x back into the expressions**:
\[
TR = 2x - 3 = 2(10) - 3 = 20 - 3 = 17 \text{ units}
\]
4. **Calculate ET**:
Since diagonals of a rectangle are equal and each diagonal bisects into two equal parts:
\[
ET = \frac{TR}{2} = \frac{17}{2} = 8.5 \text{ units}
\]
However, it seems there might be a mistake in the choices given. Please check the context of study materials for correct choices. The correct solution based on steps given should be 17 units as the length of TR, not ET.
---
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 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