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Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AC = 8 and BC = 4, what is the length of DC? (Note: the figure is not drawn to scale.) В 4 A 8

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AC = 8 and BC = 4, what is the length of DC? (Note: the figure is not drawn to scale.) В 4 A 8

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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**Problem Description:** Given right triangle \(ABC\) with altitude \(BD\) drawn to the hypotenuse \(AC\). If \(AC = 8\) and \(BC = 4\), what is the length of \(DC\)? (Note: the figure is not drawn to scale.) **Diagram Explanation:** In the provided diagram: - Triangle \(ABC\) is a right triangle, with \(\angle ABC\) being the right angle. - \(BD\) is the altitude drawn from point \(B\) perpendicular to hypotenuse \(AC\). - Point \(D\) is where the altitude \(BD\) meets \(AC\). - Segment \(AC\) (the hypotenuse) is marked as 8 units long. - Segment \(BC\) is marked as 4 units long. - Segment \(AD\) is denoted as \(8 - x\), and segment \(DC\) is denoted as \(x\). The goal is to find the length of \(DC\) (denoted as \(x\)).
Transcribed Image Text:**Problem Description:** Given right triangle \(ABC\) with altitude \(BD\) drawn to the hypotenuse \(AC\). If \(AC = 8\) and \(BC = 4\), what is the length of \(DC\)? (Note: the figure is not drawn to scale.) **Diagram Explanation:** In the provided diagram: - Triangle \(ABC\) is a right triangle, with \(\angle ABC\) being the right angle. - \(BD\) is the altitude drawn from point \(B\) perpendicular to hypotenuse \(AC\). - Point \(D\) is where the altitude \(BD\) meets \(AC\). - Segment \(AC\) (the hypotenuse) is marked as 8 units long. - Segment \(BC\) is marked as 4 units long. - Segment \(AD\) is denoted as \(8 - x\), and segment \(DC\) is denoted as \(x\). The goal is to find the length of \(DC\) (denoted as \(x\)).
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