Final answer:
To find the side EG in the similar triangles EFG and BCD, we use the proportion of corresponding sides and the given measurements to calculate EG to be approximately 0.89 units.
Step-by-step explanation:
Given that triangle EFG is similar to triangle BCD (Triangle EFG ~ BCD), the corresponding sides are in proportion. From the information provided, FG equals 18 and CD equals 4, so the scale factor from triangle BCD to triangle EFG is 18/4, which is 4.5. It is also given that EF is 3 more than BD, and BC is half of BD. Therefore, if we let the length of BD be x, we have BC as x/2 and EF as x + 3. Since BC corresponds to FG and BD corresponds to EF, we use the scale factor to find EG. Because the triangles are similar, the lengths of the sides are proportional:
BC/FG = BD/EF = CD/EG
Substituting in the known values and variables:
(x/2)/18 = x/(x+3) = 4/EG
To find EG, we solve the proportion:
4/EG = 4.5
Therefore, EG must be:
EG = 4/4.5
EG = 8/9 or approximately 0.89 units.