Alright, let's solve this step by step.
We are given that:
- [tex]\( FG = 2 \)[/tex] units
- [tex]\( FI = 7 \)[/tex] units
- [tex]\( HI = 1 \)[/tex] unit
We need to find the length of [tex]\( GH \)[/tex].
1. First, understand the relationships between the segments. We know [tex]\( FI \)[/tex] is composed of segments that include [tex]\( FG \)[/tex] and [tex]\( HI \)[/tex] plus the segment [tex]\( GH \)[/tex] that we want to find.
2. To clearly see the relationship, you can think of [tex]\( FI \)[/tex] (from F to I) as a straight path made up of [tex]\( FG \)[/tex], [tex]\( GH \)[/tex], and [tex]\( HI \)[/tex].
3. The total length of [tex]\( FI \)[/tex] is given as 7 units. To figure out how long [tex]\( GH \)[/tex] is, we need to subtract the lengths of [tex]\( FG \)[/tex] and [tex]\( HI \)[/tex] from [tex]\( FI \)[/tex].
4. Since [tex]\( FG + GH + HI = FI \)[/tex]:
[tex]\[ FG = 2 \text{ units} \][/tex]
[tex]\[ HI = 1 \text{ unit} \][/tex]
[tex]\[ FG + GH + HI = 7 \text{ units} \][/tex]
So we have:
[tex]\[ 2 + GH + 1 = 7 \][/tex]
5. Combine the known lengths:
[tex]\[ 3 + GH = 7 \][/tex]
6. Solving for [tex]\( GH \)[/tex]:
[tex]\[ GH = 7 - 3 \][/tex]
[tex]\[ GH = 4 \][/tex]
Therefore, the length of [tex]\( GH \)[/tex] is [tex]\( 4 \)[/tex] units. Thus, the correct answer is [tex]\( 4 \)[/tex] units.
