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

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:** \( GH = 8 \)