Final answer:
To find the length of DG, we can use the concept of congruent triangles and set up a proportion. Solving the proportion, we find that DG is equal to approximately 4.67 units.
Step-by-step explanation:
To find the length of segment DG, we can use the concept of congruent triangles. Since triangles GFC and AHD are congruent, we can set up the following proportion:
(CF / GC) = (AD / DH)
Substituting the given values, we have:
(18 / GC) = (32 / (GC + DG))
Now we can solve for DG. Cross multiplying, we get:
18*(GC + DG) = 32*GC
18*GC + 18*DG = 32*GC
18*DG = 14*GC
DG = (14/18)*GC
From the given information, we know that EC = 24 and CF = 18. So, GC = EC - CF = 24 - 18 = 6. Substituting this value, we find that DG = (14/18)*6 = 4.67 units.