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If [tex]FG = 2[/tex] units, [tex]FI = 7[/tex] units, and [tex]HI = 1[/tex] unit, what is [tex]GH[/tex]?

A. 3 units
B. 4 units
C. 5 units
D. 6 units

Sagot :

GinnyAnswer
To find the length of [tex]\( GH \)[/tex] given the measurements [tex]\( FG = 2 \)[/tex] units, [tex]\( FI = 7 \)[/tex] units, and [tex]\( HI = 1 \)[/tex] unit, follow these steps:

1. Understand the relationship: We are given three lengths [tex]\( FG \)[/tex], [tex]\( FI \)[/tex], and [tex]\( HI \)[/tex]. The goal is to find the length of [tex]\( GH \)[/tex].

2. Identify the points and segments: We assume [tex]\( G \)[/tex], [tex]\( H \)[/tex], and [tex]\( I \)[/tex] are collinear points with [tex]\( G \)[/tex] and [tex]\( I \)[/tex] being at the extremities and [tex]\( H \)[/tex] lying somewhere in between.

3. Consider the total distance [tex]\( FI \)[/tex]. We want to express [tex]\( FI \)[/tex] as the sum of the segments [tex]\( FG \)[/tex], [tex]\( GH \)[/tex], and [tex]\( HI \)[/tex]:
[tex]\[ FI = FG + GH + HI \][/tex]

4. Substitute the known values:
[tex]\[ 7 = 2 + GH + 1 \][/tex]

5. Simplify the equation to isolate [tex]\( GH \)[/tex]:
[tex]\[ 7 = 3 + GH \][/tex]

6. Solve for [tex]\( GH \)[/tex]:
[tex]\[ GH = 7 - 3 = 4 \][/tex]

Therefore, the length of [tex]\( GH \)[/tex] is 4 units. The correct answer is:
[tex]\[ \boxed{4 \text{ units}} \][/tex]
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