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What is the length of the dotted line in the diagram below? Round to the ne tenth. 3 す

What is the length of the dotted line in the diagram below? Round to the ne tenth. 3 す

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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**Length of the Dotted Line (Educational Content)** **Problem:** What is the length of the dotted line in the diagram below? Round to the nearest tenth. **Diagram Description:** - The diagram displays a geometric shape comprising a rectangle attached to a right-angled triangle at the bottom. - The rectangle has vertical sides measuring 7 units. - The right-angled triangle has a base of 4 units and a height of 3 units. - A dotted diagonal line spans from the top-right corner of the rectangle to the bottom-left corner of the triangle, cutting through the entire composite shape. **Steps to Solve:** 1. Identify the right-angled triangle formed by rearranging the shape. The sides of this triangle measure: - Opposite: 3 units - Adjacent: 4 units - Hypotenuse (along the base of the triangle): Use the Pythagorean theorem: \( c = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \) units 2. The dotted line in the diagram can be calculated using the Pythagorean theorem with the given vertical distance (7 units) and the hypotenuse (5 units). Therefore, we need to use the Pythagorean theorem again to solve for the dotted line: \( d = \sqrt{7^2 + 5^2} = \sqrt{49 + 25} = \sqrt{74} = 8.6 \) units (approx). **Answer:** 8.6 (Rounded to the nearest tenth) Click the "Submit Answer" button to finalize your answer. --- *Note: The calculations have to be thoroughly checked for understanding in an educational setting before finalizing the submission.*
Transcribed Image Text:**Length of the Dotted Line (Educational Content)** **Problem:** What is the length of the dotted line in the diagram below? Round to the nearest tenth. **Diagram Description:** - The diagram displays a geometric shape comprising a rectangle attached to a right-angled triangle at the bottom. - The rectangle has vertical sides measuring 7 units. - The right-angled triangle has a base of 4 units and a height of 3 units. - A dotted diagonal line spans from the top-right corner of the rectangle to the bottom-left corner of the triangle, cutting through the entire composite shape. **Steps to Solve:** 1. Identify the right-angled triangle formed by rearranging the shape. The sides of this triangle measure: - Opposite: 3 units - Adjacent: 4 units - Hypotenuse (along the base of the triangle): Use the Pythagorean theorem: \( c = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \) units 2. The dotted line in the diagram can be calculated using the Pythagorean theorem with the given vertical distance (7 units) and the hypotenuse (5 units). Therefore, we need to use the Pythagorean theorem again to solve for the dotted line: \( d = \sqrt{7^2 + 5^2} = \sqrt{49 + 25} = \sqrt{74} = 8.6 \) units (approx). **Answer:** 8.6 (Rounded to the nearest tenth) Click the "Submit Answer" button to finalize your answer. --- *Note: The calculations have to be thoroughly checked for understanding in an educational setting before finalizing the submission.*
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