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If [tex]$FG = 2$[/tex] units, [tex]$FI = 7$[/tex] units, and [tex][tex]$HI = 1$[/tex][/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], we need to understand the relationship between the given segments [tex]\(FG\)[/tex], [tex]\(FI\)[/tex], and [tex]\(HI\)[/tex]. Let's analyze the given information step-by-step.

We are given:
- [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].

First, let's identify segment [tex]\(GH\)[/tex] within the context of segment [tex]\(FI\)[/tex].
- [tex]\(FI\)[/tex] is the entire length from point [tex]\(F\)[/tex] to point [tex]\(I\)[/tex].
- Segment [tex]\(FI\)[/tex] is divided into two parts: [tex]\(FG\)[/tex] and [tex]\(GH + HI\)[/tex].

From the given lengths:
- [tex]\( FG \)[/tex] is part of the segment from [tex]\(F\)[/tex] to [tex]\(G\)[/tex].
- [tex]\( HI \)[/tex] is part of the segment from [tex]\(H\)[/tex] to [tex]\(I\)[/tex].

We need to determine [tex]\(GH\)[/tex]. We can use the total length [tex]\(FI\)[/tex] to help us find the length of [tex]\(GH\)[/tex].

To calculate [tex]\(GH\)[/tex], we can denote:
[tex]\[ FI = FG + GH + HI \][/tex]

We rearrange this to express [tex]\(GH\)[/tex]:
[tex]\[ GH = FI - (FG + HI) \][/tex]

Substitute the known values into the equation:
[tex]\[ GH = 7 - (2 + 1) \][/tex]
[tex]\[ GH = 7 - 3 \][/tex]
[tex]\[ GH = 4 \][/tex]

Therefore, the length of [tex]\(GH\)[/tex] is 4 units.

The correct answer is: 4 units
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