Answer: 54
Explanation:
Given the information that C is the midpoint of AB, D is the midpoint of AC, and E is the midpoint of AD, we can infer that these segments are bisected into two equal parts.
From the given points, we can establish the following relationships:
- CD = AC / 2
- DE = AD / 2
Furthermore, the point F is the midpoint of segment ED, and point G is the midpoint of segment EF:
- FG = EF / 2
- GH = FG / 2
Finally, the point H is the midpoint of segment DB:
- DH = DB / 2
Now let's consider the information provided. We know that DC = 72, and since D is the midpoint of AC, AC = 2 * DC = 2 * 72 = 144.
Also, since E is the midpoint of AD and DE = AD / 2, we can say that AD = 2 * DE.
Using these relationships, we can work backward to find the length of AD:
AD = 2 * DE
AD = 2 * (DC / 2)
AD = DC
So, AD = 72.
Now, considering point F as the midpoint of segment ED, we know that EF = 2 * FG. Since GH = FG / 2, we can substitute these relationships:
EF = 2 * FG
GH = FG / 2
GH = (EF / 2) / 2
Substitute EF with DE + DF:
EF = DE + DF
GH = (DE + DF) / 2
Substitute DE and DF:
GH = (DC / 2 + DC) / 2
GH = (3/2) * DC / 2
GH = (3/4) * DC
Substitute DC = 72:
GH = (3/4) * 72
GH = 54
Therefore, GH = 54 units.