https://file.aiquickdraw.com/mathbot/file/17265461587988u06hnbp.jpg

The problem states that \( R \) is the midpoint of \( QS \). It provides the following information:
- \( RS = 2x - 4 \),
- \( ST = 4x - 1 \),
- \( QT = 8x - 43 \).

We are tasked with finding the length of \( QS \).

### Step-by-step solution:

1. **Understand the midpoint condition:**
   Since \( R \) is the midpoint of \( QS \), the length of \( QS \) is twice the length of \( RS \). This gives us:
   \[
   QS = 2 \times RS = 2(2x - 4) = 4x - 8.
   \]

2. **Express \( QT \) in terms of known lengths:**
   The total length \( QT \) is the sum of \( QS \) and \( ST \). So:
   \[
   QT = QS + ST.
   \]
   Substitute the known expressions for \( QT \), \( QS \), and \( ST \):
   \[
   8x - 43 = (4x - 8) + (4x - 1).
   \]
   
3. **Simplify and solve for \( x \):**
   Combine like terms:
   \[
   8x - 43 = 4x - 8 + 4x - 1,
   \]
   \[
   8x - 43 = 8x - 9.
   \]
   Subtract \( 8x \) from both sides:
   \[
   -43 = -9.
   \]
   This is clearly not possible, which suggests an error in my interpretation or setup. Let's reassess the problem.

Since the setup seems inconsistent, please let me double-check the conditions in case I misinterpreted the figure. Would you like me to try a different approach or check any specific step?



If R is the midpoint of QS, RS = 2x - 4, ST = 4x - 1, and QT = 8x - 43, find QS.

Learn how to solve a geometry problem involving the midpoint of a segment, RS = 2x - 4, ST = 4x - 1, and QT = 8x - 43. This problem uses algebra and the midpoint theorem to determine the length of QS. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation