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
![**Question:**
The hypotenuse of a 45°-45°-90° triangle measures \(7\sqrt{2}\) units. What is the length of one leg of the triangle?
**Diagram Explanation:**
The diagram shows an isosceles right triangle (45°-45°-90° triangle). In this particular triangle:
- The two legs, which are of equal length, form the right angle.
- The hypotenuse, opposite the right angle, is labeled \(7\sqrt{2}\) units.
**Options:**
1. 7 units
2. \(7\sqrt{2}\) units
3. 14 units
4. \(14\sqrt{2}\) units
**Explanation:**
In a 45°-45°-90° triangle, the hypotenuse is \( \sqrt{2} \) times the length of each leg. Given the hypotenuse is \( 7\sqrt{2} \) units, we can find the length of one leg by dividing the length of the hypotenuse by \( \sqrt{2} \):
\[
\text{Leg length} = \frac{7\sqrt{2}}{\sqrt{2}} = 7 \text{ units}
\]
The correct answer is:
- 7 units](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1fefc4e4-0fc1-4d3a-92e0-1dd9cbc9acda%2F6a61e8ad-7b8e-48f1-982d-f9ec30a56dad%2F5m1weyj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
The hypotenuse of a 45°-45°-90° triangle measures \(7\sqrt{2}\) units. What is the length of one leg of the triangle?
**Diagram Explanation:**
The diagram shows an isosceles right triangle (45°-45°-90° triangle). In this particular triangle:
- The two legs, which are of equal length, form the right angle.
- The hypotenuse, opposite the right angle, is labeled \(7\sqrt{2}\) units.
**Options:**
1. 7 units
2. \(7\sqrt{2}\) units
3. 14 units
4. \(14\sqrt{2}\) units
**Explanation:**
In a 45°-45°-90° triangle, the hypotenuse is \( \sqrt{2} \) times the length of each leg. Given the hypotenuse is \( 7\sqrt{2} \) units, we can find the length of one leg by dividing the length of the hypotenuse by \( \sqrt{2} \):
\[
\text{Leg length} = \frac{7\sqrt{2}}{\sqrt{2}} = 7 \text{ units}
\]
The correct answer is:
- 7 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