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:

$\frac{EF}{EC}=\frac{EG}{ED}$

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

$\begin{gathered} \frac{EF}{EF+FC}=\frac{EG}{EG+GD}\\ \\ \frac{28.1}{28.1+FC}=\frac{16.9}{16.9+10.1}\\ \\ \frac{28.1}{28.1+FC}=\frac{16.9}{27}\\ \\ 28.1+FC=\frac{28.1\cdot27}{16.9}\\ \\ 28.1+FC=44.9\\ \\ FC=44.9-28.1\\ \\ FC=16.8 \end{gathered}$

Therefore the length of FC is 16.8 units.