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In the diagram below of rectangle RSTU, diagonals RT and SU intersect at O. If RT = 6x +4 and SO = 7x – 6, what is the length %3D of US? Answer: US = Submit Answer R

In the diagram below of rectangle RSTU, diagonals RT and SU intersect at O. If RT = 6x +4 and SO = 7x – 6, what is the length %3D of US? Answer: US = Submit Answer R

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 Statement: Rectangle Diagonals Intersection In the diagram below of rectangle \( RSTU \), diagonals \( \overline{RT} \) and \( \overline{SU} \) intersect at \( O \). ![Rectangle RSTU](diagram) If \( \overline{RT} = 6x + 4 \) and \( \overline{SO} = 7x - 6 \), what is the length of \( \overline{US} \)? **Diagram Explanation:** - The diagram illustrates a rectangle labeled \( RSTU \) with its vertices \( R, S, T, \) and \( U \) forming the rectangle in a clockwise manner starting from the bottom left corner. - Diagonals \( \overline{RT} \) and \( \overline{SU} \) intersect at point \( O \), dividing each diagonal into two equal segments. **Mathematical Details:** 1. Given diagonal \( \overline{RT} = 6x + 4 \) 2. Given segment \( \overline{SO} = 7x - 6 \) 3. Since diagonals of a rectangle bisect each other, \( \overline{SO} \) is half of diagonal \( \overline{SU} \). **Problem:** Determine the length of \( \overline{US} \). **Answer Box:** ___ Answer: \( \overline{US} = \) __________ ___ [Submit Answer Button] --- This educational content invites learners to solve for the length of \( \overline{US} \) using the given algebraic expressions for the diagonals and segment \( \overline{SO} \).
Transcribed Image Text:### Problem Statement: Rectangle Diagonals Intersection In the diagram below of rectangle \( RSTU \), diagonals \( \overline{RT} \) and \( \overline{SU} \) intersect at \( O \). ![Rectangle RSTU](diagram) If \( \overline{RT} = 6x + 4 \) and \( \overline{SO} = 7x - 6 \), what is the length of \( \overline{US} \)? **Diagram Explanation:** - The diagram illustrates a rectangle labeled \( RSTU \) with its vertices \( R, S, T, \) and \( U \) forming the rectangle in a clockwise manner starting from the bottom left corner. - Diagonals \( \overline{RT} \) and \( \overline{SU} \) intersect at point \( O \), dividing each diagonal into two equal segments. **Mathematical Details:** 1. Given diagonal \( \overline{RT} = 6x + 4 \) 2. Given segment \( \overline{SO} = 7x - 6 \) 3. Since diagonals of a rectangle bisect each other, \( \overline{SO} \) is half of diagonal \( \overline{SU} \). **Problem:** Determine the length of \( \overline{US} \). **Answer Box:** ___ Answer: \( \overline{US} = \) __________ ___ [Submit Answer Button] --- This educational content invites learners to solve for the length of \( \overline{US} \) using the given algebraic expressions for the diagonals and segment \( \overline{SO} \).
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