Answer:
To summarize, the correct answer is:
DG ≈ 18.375
Explanation:
To find the value of DG, we can use the properties of a perpendicular bisector.
1. Given that FE is the perpendicular bisector of DG, we know that DF and FG are congruent segments.
2. DF is given as 14 units.
3. FG is represented as 4x, where x is an unknown value.
4. DE is given as 1.25x.
Since DF and FG are congruent, we can set up the following equation:
14 = 4x
To solve for x, we divide both sides of the equation by 4:
14/4 = x
x = 3.5
Now, we can substitute the value of x into the equation for DE:
DE = 1.25x
DE = 1.25 * 3.5
DE = 4.375
Since DG is the sum of DE and FG, we can calculate DG as follows:
DG = DE + FG
DG = 4.375 + 4x
DG = 4.375 + 4(3.5)
DG = 4.375 + 14
DG = 18.375
Therefore, the value of DG is approximately 18.375.