5. An Olympic-size swimming pool is approximately 50 meters long by 25 meters wide. What distance will a swimmer travel if they swim from one comer to the opposite? 25
5. An Olympic-size swimming pool is approximately 50 meters long by 25 meters wide. What distance will a swimmer travel if they swim from one comer to the opposite? 25
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
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![### Problem Statement:
An Olympic-size swimming pool is approximately 50 meters long by 25 meters wide. What distance will a swimmer travel if they swim from one corner to the opposite?
### Explanation:
To determine the distance a swimmer will travel if they swim diagonally from one corner of the pool to the opposite, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle:
\[ a^2 + b^2 = c^2 \]
Where:
- \( a \) and \( b \) are the lengths of the two shorter sides of the triangle.
- \( c \) is the length of the hypotenuse (the side opposite the right angle).
In this problem, the length and the width of the pool represent the two shorter sides of a right-angled triangle, and the distance the swimmer travels represents the hypotenuse. Here, \( a = 50 \) meters and \( b = 25 \) meters.
### Calculation:
\[ c = \sqrt{a^2 + b^2} \]
\[ c = \sqrt{50^2 + 25^2} \]
\[ c = \sqrt{2500 + 625} \]
\[ c = \sqrt{3125} \]
\[ c \approx 55.90 \text{ meters} \]
So, the distance the swimmer will travel diagonally from one corner of the pool to the opposite is approximately 55.90 meters.
### Diagram Explanation:
The problem includes a diagram of a rectangle representing the swimming pool. The rectangle is labeled with its dimensions: 50 meters (length) and 25 meters (width). A dashed line runs diagonally from one corner of the rectangle to the opposite corner, illustrating the swimmer's path. The diagonal represents the hypotenuse of the right-angled triangle formed by the length and width of the pool.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e0f9904-2fe6-4bf6-82c9-6f19ce3adc31%2Fd753ff8f-cc2c-4762-afb3-d429a87ab44c%2Fo6wbmc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
An Olympic-size swimming pool is approximately 50 meters long by 25 meters wide. What distance will a swimmer travel if they swim from one corner to the opposite?
### Explanation:
To determine the distance a swimmer will travel if they swim diagonally from one corner of the pool to the opposite, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle:
\[ a^2 + b^2 = c^2 \]
Where:
- \( a \) and \( b \) are the lengths of the two shorter sides of the triangle.
- \( c \) is the length of the hypotenuse (the side opposite the right angle).
In this problem, the length and the width of the pool represent the two shorter sides of a right-angled triangle, and the distance the swimmer travels represents the hypotenuse. Here, \( a = 50 \) meters and \( b = 25 \) meters.
### Calculation:
\[ c = \sqrt{a^2 + b^2} \]
\[ c = \sqrt{50^2 + 25^2} \]
\[ c = \sqrt{2500 + 625} \]
\[ c = \sqrt{3125} \]
\[ c \approx 55.90 \text{ meters} \]
So, the distance the swimmer will travel diagonally from one corner of the pool to the opposite is approximately 55.90 meters.
### Diagram Explanation:
The problem includes a diagram of a rectangle representing the swimming pool. The rectangle is labeled with its dimensions: 50 meters (length) and 25 meters (width). A dashed line runs diagonally from one corner of the rectangle to the opposite corner, illustrating the swimmer's path. The diagonal represents the hypotenuse of the right-angled triangle formed by the length and width of the pool.
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