please help ### Problem 29: Midpoints in Triangle Geometry**Problem Statement:**In triangle \( GHJ \) below, points \( A \), \( B \), and \( C \) are midpoints of the sides.![Triangle Diagram](image_url_placeholder) The diagram shows triangle \( GHJ \) with an inner triangle \( ABC \) formed by connecting the midpoints of the sides. Here, \( A \) is the midpoint of \( GH \), \( B \) is the midpoint of \( HJ \), and \( C \) is the midpoint of \( GJ \).**Given:**- \( AB = 3x + 8 \)- \( GJ = 2x + 24 \)**Question:**What is the length of \( AB \)?**Options:**- 8- 14- 24- 28### Detailed Explanation of the Diagram:The diagram is essential for understanding the placement of points and segments in this midpoints problem:- The largest triangle is \( GHJ \).- Points \( A \), \( B \), and \( C \) are aligned such that each divides the sides \( GH \), \( HJ \), and \( GJ \) into equal segments.- The smaller triangle \( ABC \) is formed inside \( GHJ \) by connecting these midpoints.### Steps to Solve:1. **Understanding Midpoints:** - As \( A \) is the midpoint of \( GH \), \( B \) is the midpoint of \( HJ \), and \( C \) is the midpoint of \( GJ \), each mid-segment (e.g., \( AB \)) is half the length of its corresponding base segment (in this case, \( GJ \)).2. **Setting Up the Equation:** - Given that \( AB \) is half of \( GJ \): \[ AB = \frac{1}{2} GJ \] - Substituting the given expressions: \[ 3x + 8 = \frac{1}{2} (2x + 24) \]3. **Solving the Equation:** - Simplifying the right-hand side: \[ 3x + 8 = x + 12 \] - Rearranging terms to isolate \( x \

Name: please help ### Problem 29: Midpoints in Triangle Geometry**Problem St
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: please help ### Problem 29: Midpoints in Triangle Geometry**Problem Statement:**In triangle \( GHJ \) below, points \( A \), \( B \), and \( C \) are midpoints of the sides.![Triangle Diagram](image_url_placeholder) The diagram shows triangle \( GHJ