Question

Find FG. The diagram is not to scale.

Answer 1

FG = FE
3n - 4 = n + 8
2n = 12
  n = 6

FG = 3(6) - 4
FG = 18 - 4
FG = 14

answer
14

Answer 2

We can use similar triangles.  Since we have two right triangles that have two equal angles, that means all 3 angles are congruent.  

Thus triangle EDF is similar to GDF.

Then we can set up a proportion.

(3n-4)/(n+8) = DF/DF   (where DF is the length of they hypotenuse, but since they are the same length, DF/DF is just equal to 1.)

So:  (3n-4)/(n+8) = 1

Now just solve:  3n - 4 = n + 8

2n = 12

n = 6

Therefore FG = 3(6) - 4 = 18 - 4 = 14

FG = 14