### Pythagorean Theorem Application **Problem Statement:** A right angle is made where the top of a ladder meets the top of the slide as shown in the picture below. What is the length of the slide? **Diagram:** - The image shows a right-angled triangle where: - One leg (representing the vertical height of the slide) is labeled as 5 meters. - The other leg (representing the horizontal distance from the bottom of the ladder to the bottom of the slide) is labeled as 13 meters. - The hypotenuse (representing the length of the slide) is denoted with a question mark (?). **Given Options:** - **A. \( \sqrt{8} \) meters** - **B. 8 meters** - **C. 12 meters** - **D. \( \sqrt{194} \) meters** **Objective:** Determine the length of the slide. ### Explanation: To find the length of the slide (the hypotenuse of the right triangle), apply the Pythagorean theorem: \[ a^2 + b^2 = c^2 \] Where: - \( a \) and \( b \) are the lengths of the two legs of the right triangle. - \( c \) is the length of the hypotenuse. Here, let: - \( a = 5 \) meters - \( b = 13 \) meters - \( c \) is the length of the slide we need to find. Substitute the known values into the Pythagorean theorem: \[ 5^2 + 13^2 = c^2 \] Calculate the squares: \[ 25 + 169 = c^2 \] Combine the values: \[ 194 = c^2 \] To find \( c \), take the square root of both sides: \[ c = \sqrt{194} \] Therefore, the length of the slide is \( \sqrt{194} \) meters, which corresponds to: **Correct Answer: D. \( \sqrt{194} \) meters** **Answer Choices:** - O A - O B - O C - ● D
### Pythagorean Theorem Application **Problem Statement:** A right angle is made where the top of a ladder meets the top of the slide as shown in the picture below. What is the length of the slide? **Diagram:** - The image shows a right-angled triangle where: - One leg (representing the vertical height of the slide) is labeled as 5 meters. - The other leg (representing the horizontal distance from the bottom of the ladder to the bottom of the slide) is labeled as 13 meters. - The hypotenuse (representing the length of the slide) is denoted with a question mark (?). **Given Options:** - **A. \( \sqrt{8} \) meters** - **B. 8 meters** - **C. 12 meters** - **D. \( \sqrt{194} \) meters** **Objective:** Determine the length of the slide. ### Explanation: To find the length of the slide (the hypotenuse of the right triangle), apply the Pythagorean theorem: \[ a^2 + b^2 = c^2 \] Where: - \( a \) and \( b \) are the lengths of the two legs of the right triangle. - \( c \) is the length of the hypotenuse. Here, let: - \( a = 5 \) meters - \( b = 13 \) meters - \( c \) is the length of the slide we need to find. Substitute the known values into the Pythagorean theorem: \[ 5^2 + 13^2 = c^2 \] Calculate the squares: \[ 25 + 169 = c^2 \] Combine the values: \[ 194 = c^2 \] To find \( c \), take the square root of both sides: \[ c = \sqrt{194} \] Therefore, the length of the slide is \( \sqrt{194} \) meters, which corresponds to: **Correct Answer: D. \( \sqrt{194} \) meters** **Answer Choices:** - O A - O B - O C - ● D
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![### Pythagorean Theorem Application
**Problem Statement:**
A right angle is made where the top of a ladder meets the top of the slide as shown in the picture below. What is the length of the slide?
**Diagram:**
- The image shows a right-angled triangle where:
- One leg (representing the vertical height of the slide) is labeled as 5 meters.
- The other leg (representing the horizontal distance from the bottom of the ladder to the bottom of the slide) is labeled as 13 meters.
- The hypotenuse (representing the length of the slide) is denoted with a question mark (?).
**Given Options:**
- **A. \( \sqrt{8} \) meters**
- **B. 8 meters**
- **C. 12 meters**
- **D. \( \sqrt{194} \) meters**
**Objective:**
Determine the length of the slide.
### Explanation:
To find the length of the slide (the hypotenuse of the right triangle), apply the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
Where:
- \( a \) and \( b \) are the lengths of the two legs of the right triangle.
- \( c \) is the length of the hypotenuse.
Here, let:
- \( a = 5 \) meters
- \( b = 13 \) meters
- \( c \) is the length of the slide we need to find.
Substitute the known values into the Pythagorean theorem:
\[ 5^2 + 13^2 = c^2 \]
Calculate the squares:
\[ 25 + 169 = c^2 \]
Combine the values:
\[ 194 = c^2 \]
To find \( c \), take the square root of both sides:
\[ c = \sqrt{194} \]
Therefore, the length of the slide is \( \sqrt{194} \) meters, which corresponds to:
**Correct Answer: D. \( \sqrt{194} \) meters**
**Answer Choices:**
- O A
- O B
- O C
- ● D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F492f8302-2af6-4a90-9bdc-ae62d55032ea%2F3bbd445d-783f-4464-a814-2bae176d84e7%2F0be6aeo.jpeg&w=3840&q=75)
Transcribed Image Text:### Pythagorean Theorem Application
**Problem Statement:**
A right angle is made where the top of a ladder meets the top of the slide as shown in the picture below. What is the length of the slide?
**Diagram:**
- The image shows a right-angled triangle where:
- One leg (representing the vertical height of the slide) is labeled as 5 meters.
- The other leg (representing the horizontal distance from the bottom of the ladder to the bottom of the slide) is labeled as 13 meters.
- The hypotenuse (representing the length of the slide) is denoted with a question mark (?).
**Given Options:**
- **A. \( \sqrt{8} \) meters**
- **B. 8 meters**
- **C. 12 meters**
- **D. \( \sqrt{194} \) meters**
**Objective:**
Determine the length of the slide.
### Explanation:
To find the length of the slide (the hypotenuse of the right triangle), apply the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
Where:
- \( a \) and \( b \) are the lengths of the two legs of the right triangle.
- \( c \) is the length of the hypotenuse.
Here, let:
- \( a = 5 \) meters
- \( b = 13 \) meters
- \( c \) is the length of the slide we need to find.
Substitute the known values into the Pythagorean theorem:
\[ 5^2 + 13^2 = c^2 \]
Calculate the squares:
\[ 25 + 169 = c^2 \]
Combine the values:
\[ 194 = c^2 \]
To find \( c \), take the square root of both sides:
\[ c = \sqrt{194} \]
Therefore, the length of the slide is \( \sqrt{194} \) meters, which corresponds to:
**Correct Answer: D. \( \sqrt{194} \) meters**
**Answer Choices:**
- O A
- O B
- O C
- ● D
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education