Answer:
FG = 16
Step-by-step explanation:
The triangles EFG and EHG are congruent because they share the side EG and they have the same interior angles.
If they are congruent the lengths of the corresponding sides are equal, so we can write the following equation:
FG = GH
Then, subtitute FG = x + 11 and GH = 3x + 1 to get:
x + 11 = 3x + 1
So, solving for x, we get:
x + 11 = 3x + 1
x + 11 - 1 = 3x + 1 - 1
x + 10 = 3x
x + 10 - x = 3x - x
10 = 2x
10/2 = 2x/2
5 = x
Then, replacing x by 5, we get that FG is equal to:
FG = x + 11
FG = 5 + 11
FG = 16
So, the answer is FG = 16