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 14: Use the Pythagorean theorem to find the measure of side \( x \).**
A right triangle is shown with one side measuring 20 cm, another side measuring 15 cm, and the hypotenuse labeled \( x \).
**Answer Choices:**
- A) 35
- B) 25
- C) 625
- D) 45
### Explanation
In a right triangle, the Pythagorean theorem is expressed as:
\[ a^2 + b^2 = c^2 \]
Where \( a \) and \( b \) are the lengths of the legs, and \( c \) is the length of the hypotenuse. Here, the lengths of the legs are 15 cm and 20 cm, and \( x \) is the hypotenuse.
Substitute the given lengths into the equation:
\[ 15^2 + 20^2 = x^2 \]
Calculate:
\[ 225 + 400 = x^2 \]
\[ 625 = x^2 \]
Taking the square root of both sides gives:
\[ x = 25 \]
Therefore, the correct answer is **B) 25**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35e0e75f-e8c2-4dab-b2c9-b1b559720d41%2F6e2459d4-c546-42a6-9bc8-3df067caff48%2Fuxaktdd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 14: Use the Pythagorean theorem to find the measure of side \( x \).**
A right triangle is shown with one side measuring 20 cm, another side measuring 15 cm, and the hypotenuse labeled \( x \).
**Answer Choices:**
- A) 35
- B) 25
- C) 625
- D) 45
### Explanation
In a right triangle, the Pythagorean theorem is expressed as:
\[ a^2 + b^2 = c^2 \]
Where \( a \) and \( b \) are the lengths of the legs, and \( c \) is the length of the hypotenuse. Here, the lengths of the legs are 15 cm and 20 cm, and \( x \) is the hypotenuse.
Substitute the given lengths into the equation:
\[ 15^2 + 20^2 = x^2 \]
Calculate:
\[ 225 + 400 = x^2 \]
\[ 625 = x^2 \]
Taking the square root of both sides gives:
\[ x = 25 \]
Therefore, the correct answer is **B) 25**.
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