Answer:
EF = 18
Explanation:
Given similar triangles DEF and JHI, midpoints G and K of sides DE and HI, with sides marked GF=9, EF=x+8, KI=14, HI=3x-2, you want to know the length of EF.
Proportion
Corresponding sides in similar triangles are proportional. This means ...
EF/GF = HI/KI
(x+8)/9 = (3x-2)/14 . . . . substitute given values
14(x +8) = 9(3x -2) . . . . multiply by 14·9
14x +112 = 27x -18 . . . . eliminate parentheses
130 = 13x . . . . . . . . . . . add 18-14x
10 = x . . . . . . . . . . . . . divide by 13
Now, we can find EF:
EF = x+8 = 10 +8
EF = 18