Homework Help is Here – Start Your Trial Now!
Math
Geometry
18 Find the length of the hypotenuse of this triangle. FA A. 12-√√2cm B. 24 cm 12 cm 12 cm D. 2√T2 cm

18 Find the length of the hypotenuse of this triangle. FA A. 12-√√2cm B. 24 cm 12 cm 12 cm D. 2√T2 cm

Elementary Geometry For College Students, 7e
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
See similar textbooks
icon
Related questions
Question
## Geometry Problem: Finding the Length of the Hypotenuse ### Question: **Find the length of the hypotenuse of this triangle.** ### Diagram: A right-angled triangle is depicted with one leg labeled as 12 cm. There are no other specific measurements or angles provided except for the right angle. ### Options: A. \( 12\sqrt{2} \) cm B. 24 cm C. 12 cm D. \( 2\sqrt{12} \) cm In the provided diagram, a right angle is indicated at one of the corners, specifying it as a right triangle. Since we are to find the length of the hypotenuse, we need to apply the Pythagorean theorem, which is stated as: \[ a^2 + b^2 = c^2 \] For a right-angled triangle: - \( a \) and \( b \) are the legs (one of which is given as 12 cm), - \( c \) is the hypotenuse. However, from the context of provided options and the image, it appears that the focus is more on recognizing possible answers rather than calculations, indicating an understanding of standard right triangle properties. ### Explained Correct Answer: From the options given, \( \mathbf{A.\: 12\sqrt{2}\: cm} \) is the most logical and correct choice for the hypotenuse of this triangle, according to standard right triangle properties where: \[ \text{Hypotenuse} = a\sqrt{2} \] for an isosceles right triangle. ##### Note: - The incorrect answer was marked, indicating that understanding and careful selection among choices are vital. The incorrect response marked was option C: 12 cm.
Transcribed Image Text:## Geometry Problem: Finding the Length of the Hypotenuse ### Question: **Find the length of the hypotenuse of this triangle.** ### Diagram: A right-angled triangle is depicted with one leg labeled as 12 cm. There are no other specific measurements or angles provided except for the right angle. ### Options: A. \( 12\sqrt{2} \) cm B. 24 cm C. 12 cm D. \( 2\sqrt{12} \) cm In the provided diagram, a right angle is indicated at one of the corners, specifying it as a right triangle. Since we are to find the length of the hypotenuse, we need to apply the Pythagorean theorem, which is stated as: \[ a^2 + b^2 = c^2 \] For a right-angled triangle: - \( a \) and \( b \) are the legs (one of which is given as 12 cm), - \( c \) is the hypotenuse. However, from the context of provided options and the image, it appears that the focus is more on recognizing possible answers rather than calculations, indicating an understanding of standard right triangle properties. ### Explained Correct Answer: From the options given, \( \mathbf{A.\: 12\sqrt{2}\: cm} \) is the most logical and correct choice for the hypotenuse of this triangle, according to standard right triangle properties where: \[ \text{Hypotenuse} = a\sqrt{2} \] for an isosceles right triangle. ##### Note: - The incorrect answer was marked, indicating that understanding and careful selection among choices are vital. The incorrect response marked was option C: 12 cm.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer