Answer: The correct option is (B) 12.
Step-by-step explanation: Given that D is the mid point of the line segment EG, where
\(ED=x-5,~~DG=4x-38.\)
We are to find the length of EG.
Since D is the midpoint of the segment EG, so we must have
\(ED=DG\\\\\Rightarrow x-5=4x-38\\\\\Rightarrow 4x-x=-5+38\\\\\Rightarrow 3x=33\\\\\Rightarrow x=\dfrac{33}{3}\\\\\Rightarrow x=11.\)
Therefore, the length of EG is given by
\(ED+DG\\\\=(x-5)+(4x-38)\\\\=5x-43\\\\=5\times11-43\\\\=55-43\\\\=12.\)
Thus, the required length of EG is 12 units.
Option (B) is CORRECT.
