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
![**Problem Statement:**
Find the length \( x \).
**Diagram Explanation:**
The image displays a right triangle with one side extended, forming a larger right triangle.
- The smaller right triangle has a base of 4 units and an adjacent side of 2 units, forming a right angle.
- The larger triangle shares a hypotenuse with the smaller triangle labeled as 7 units.
- The hypotenuse of the larger triangle is labeled \( x \).
To find \( x \), apply the Pythagorean theorem for the larger triangle:
\( 4 + 2 = 6 \).
Use:
\[ \text{Hypotenuse}^2 = \text{Longer side}^2 + 7^2 \]
Thus:
\[ x = \sqrt{6^2 + 7^2} \]
Calculate:
\[ x = \sqrt{36 + 49} \]
\[ x = \sqrt{85} \]
Therefore, \( x = \sqrt{85} \approx 9.22 \) units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa640d10e-8ae6-46bb-ba59-891c0500cee7%2F6b5ca5d9-7956-4a30-a8ea-f09b3b9d5168%2Fx6m53kj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the length \( x \).
**Diagram Explanation:**
The image displays a right triangle with one side extended, forming a larger right triangle.
- The smaller right triangle has a base of 4 units and an adjacent side of 2 units, forming a right angle.
- The larger triangle shares a hypotenuse with the smaller triangle labeled as 7 units.
- The hypotenuse of the larger triangle is labeled \( x \).
To find \( x \), apply the Pythagorean theorem for the larger triangle:
\( 4 + 2 = 6 \).
Use:
\[ \text{Hypotenuse}^2 = \text{Longer side}^2 + 7^2 \]
Thus:
\[ x = \sqrt{6^2 + 7^2} \]
Calculate:
\[ x = \sqrt{36 + 49} \]
\[ x = \sqrt{85} \]
Therefore, \( x = \sqrt{85} \approx 9.22 \) 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
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