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

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

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
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### Geometry Problem: Finding the Hypotenuse #### Problem Statement: 15) Find the length of the hypotenuse of this triangle. #### Diagram Description: The diagram is a right-angled triangle with one angle marked as \(45^\circ\). One of the legs of the triangle, adjacent to the \(45^\circ\) angle, is labeled \(12\) cm. #### Answer Options: A. \( 12\sqrt{2} \, \text{cm} \) B. \( 24 \, \text{cm} \) C. \( 12 \, \text{cm} \) (marked incorrect with a cross) D. \( 2\sqrt{12} \, \text{cm} \) #### Explanation: To find the hypotenuse of a right-angled triangle with a \(45^\circ\) angle, we can use the property that in a 45-45-90 triangle, the hypotenuse is \( \sqrt{2} \) times the length of each leg. Given: - One leg \( = 12 \, \text{cm} \) Therefore, the hypotenuse \( = 12 \sqrt{2} \, \text{cm} \) So the correct answer is: A. \( 12\sqrt{2} \, \text{cm} \)
Transcribed Image Text:### Geometry Problem: Finding the Hypotenuse #### Problem Statement: 15) Find the length of the hypotenuse of this triangle. #### Diagram Description: The diagram is a right-angled triangle with one angle marked as \(45^\circ\). One of the legs of the triangle, adjacent to the \(45^\circ\) angle, is labeled \(12\) cm. #### Answer Options: A. \( 12\sqrt{2} \, \text{cm} \) B. \( 24 \, \text{cm} \) C. \( 12 \, \text{cm} \) (marked incorrect with a cross) D. \( 2\sqrt{12} \, \text{cm} \) #### Explanation: To find the hypotenuse of a right-angled triangle with a \(45^\circ\) angle, we can use the property that in a 45-45-90 triangle, the hypotenuse is \( \sqrt{2} \) times the length of each leg. Given: - One leg \( = 12 \, \text{cm} \) Therefore, the hypotenuse \( = 12 \sqrt{2} \, \text{cm} \) So the correct answer is: A. \( 12\sqrt{2} \, \text{cm} \)
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