Final answer:
To find the length of GI, we can set up a proportion using the given values. By cross multiplying and simplifying the equation, we can solve for GI. The length of GI is approximately 8.57.
Step-by-step explanation:
In order to find the length of GI, we need to use the concept of proportional triangles. Since FI = 6 and IH = 20, we can set up the proportion:
FI / GI = IH / HI
Substituting the known values, we get:
6 / GI = 20 / (GI + 20)
Cross multiplying and simplifying the equation, we find:
6(GI + 20) = 20(GI)
Expanding and rearranging the equation, we get:
6GI + 120 = 20GI
Subtracting 6GI from both sides, we find:
120 = 14GI
Dividing both sides by 14, we find:
GI = 120 / 14 = 8.57
Therefore, the length of GI is approximately 8.57. Since none of the given answer choices match this value, none of the options provided are correct.