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
Related questions
Question
![Title: Finding Segment Length in a Rectangle
**Topic:** Properties of Parallelograms
In this exercise, we are given a rectangle named \( RSTU \) and tasked with finding the length of segment \( ST \).
### Diagram Explanation
- The rectangle is oriented diagonally.
- **Vertices:**
- \( U \) is at the top, connected to \( R \).
- \( T \) is at the bottom, connected to \( S \).
- **Side Lengths:**
- The top side, \( UR \), is given as \( 3a - 58 \).
- The left side, \( TS \), is given as \( 4a - 85 \).
- **Find:**
- \( ST \) is to be calculated with given expressions for other side lengths.
### Task
Calculate the length of \( ST \) by using the properties of parallelograms and rectangles. Rectangles have opposite sides that are equal, so set the expression for \( UR \) equal to that for \( TS \):
\[ 3a - 58 = 4a - 85 \]
### Solution Steps
1. Solve the equation to find the value of \( a \).
2. Substitute the value of \( a \) back into either expression to find \( ST \).
Once calculated, enter the length of \( ST \) into the provided input box and click "Submit" to check your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46e25c80-76d1-40fc-b8ee-938f2c7ceeae%2F1eed3c8d-e17a-420a-aa0a-2ec1ab97bba3%2F26nes0s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Title: Finding Segment Length in a Rectangle
**Topic:** Properties of Parallelograms
In this exercise, we are given a rectangle named \( RSTU \) and tasked with finding the length of segment \( ST \).
### Diagram Explanation
- The rectangle is oriented diagonally.
- **Vertices:**
- \( U \) is at the top, connected to \( R \).
- \( T \) is at the bottom, connected to \( S \).
- **Side Lengths:**
- The top side, \( UR \), is given as \( 3a - 58 \).
- The left side, \( TS \), is given as \( 4a - 85 \).
- **Find:**
- \( ST \) is to be calculated with given expressions for other side lengths.
### Task
Calculate the length of \( ST \) by using the properties of parallelograms and rectangles. Rectangles have opposite sides that are equal, so set the expression for \( UR \) equal to that for \( TS \):
\[ 3a - 58 = 4a - 85 \]
### Solution Steps
1. Solve the equation to find the value of \( a \).
2. Substitute the value of \( a \) back into either expression to find \( ST \).
Once calculated, enter the length of \( ST \) into the provided input box and click "Submit" to check your answer.
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