Question

If D is the midpoint of EG, find the length of EG.

A.

6 B. 12 C. 18 D. 21

Answer 1

D is midpoint => x-5=4x-38
x=11 => EG = 2(11-5)=12
The answer is B

Answer 2

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=(33)/(3)\\\\\Rightarrow x=11.`

Therefore, the length of EG is given by

`ED+DG\\\\=(x-5)+(4x-38)\\\\=5x-43\\\\=5*11-43\\\\=55-43\\\\=12.`

Thus, the required length of EG is 12 units.

Option (B) is CORRECT.