Question
Question The points \( \mathrm{F}, \mathrm{G}, \mathrm{H} \) and I all lie on the same line segment, in that order, such that the ratio of \( F G: G H: H I \) is equal to \( 5: 4: 3 \). If \( F I=24 \), find \( G H \). Answer Attempt 1 out of 3 \( G H=\square \) Submit Answer
Ask by Nichols Hanson. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( GH = 8 \)
Solution
To solve the problem, let's break down the information given:
1. **Ratio Breakdown:**
- The lengths are in the ratio \( FG : GH : HI = 5 : 4 : 3 \).
- Let’s represent each segment with a multiplier \( x \):
- \( FG = 5x \)
- \( GH = 4x \)
- \( HI = 3x \)
2. **Total Length:**
- The total length \( FI \) is the sum of all segments:
\[
FI = FG + GH + HI = 5x + 4x + 3x = 12x
\]
- Given that \( FI = 24 \):
\[
12x = 24 \quad \Rightarrow \quad x = 2
\]
3. **Finding \( GH \):**
- Substitute \( x = 2 \) into \( GH \):
\[
GH = 4x = 4 \times 2 = 8
\]
**Answer:** \( GH = 8 \)
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Extra Insights
To find \(GH\), we can start by representing the lengths of \(FG\), \(GH\), and \(HI\) in terms of a variable that reflects their ratio. Let's denote the lengths as \(5x\), \(4x\), and \(3x\) respectively, based on the given ratio \(5:4:3\). Now, the total length from \(F\) to \(I\) is the sum of all three segments: \[ FG + GH + HI = 5x + 4x + 3x = 12x \] Given that \(FI = 24\), we have: \[ 12x = 24 \] From this, we can solve for \(x\): \[ x = \frac{24}{12} = 2 \] Now we can calculate \(GH\): \[ GH = 4x = 4 \times 2 = 8 \] So, \[ GH = 8 \] Thus, the final answer is: \(GH = 8\)
