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
Solve for x
![**Solve for x**
The image displays a right-angled triangle with the following dimensions:
- One of the legs is labeled "10."
- The other leg is labeled "24."
- The hypotenuse, opposite the right angle, is labeled "x."
There is a prompt "Solve for x" with an equation box below, where the value of x should be calculated.
**Explanation of Diagram:**
This is a classic right-angled triangle problem, where you can use the Pythagorean theorem to find the length of the hypotenuse. According to the Pythagorean theorem, the square of the hypotenuse (x) is equal to the sum of the squares of the other two sides. Hence, the equation to solve is:
\[ x^2 = 10^2 + 24^2 \]
\[ x^2 = 100 + 576 \]
\[ x^2 = 676 \]
\[ x = \sqrt{676} \]
\[ x = 26 \]
So, the value of x is 26.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3727559b-c428-407a-939e-3225a150d3fe%2Fd2925d7a-0d2e-4e8f-970d-0f5dd0817e52%2Fbms81ug_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve for x**
The image displays a right-angled triangle with the following dimensions:
- One of the legs is labeled "10."
- The other leg is labeled "24."
- The hypotenuse, opposite the right angle, is labeled "x."
There is a prompt "Solve for x" with an equation box below, where the value of x should be calculated.
**Explanation of Diagram:**
This is a classic right-angled triangle problem, where you can use the Pythagorean theorem to find the length of the hypotenuse. According to the Pythagorean theorem, the square of the hypotenuse (x) is equal to the sum of the squares of the other two sides. Hence, the equation to solve is:
\[ x^2 = 10^2 + 24^2 \]
\[ x^2 = 100 + 576 \]
\[ x^2 = 676 \]
\[ x = \sqrt{676} \]
\[ x = 26 \]
So, the value of x is 26.
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