Question

In the diagram below, GD = 10.1,EF = 28.1, and EG = 16.9. Find the lengthof FC. Round your answer to the nearest tenthif necessary

Answer 1

Since FG is parallel to CD, the triangles EFG and ECD are similar by case AA.

Therefore, we can write the following proportion:

`(EF)/(EC)=(EG)/(ED)`

Rewriting the segments and using the given values, we have:

`\begin{gathered} (EF)/(EF+FC)=(EG)/(EG+GD)\\ \\ (28.1)/(28.1+FC)=(16.9)/(16.9+10.1)\\ \\ (28.1)/(28.1+FC)=(16.9)/(27)\\ \\ 28.1+FC=(28.1\cdot27)/(16.9)\\ \\ 28.1+FC=44.9\\ \\ FC=44.9-28.1\\ \\ FC=16.8 \end{gathered}`

Therefore the length of FC is 16.8 units.