To obtain the value of x, the following steps are necessary:
Step 1: Since both triangles CDE and FGE are similar, the following ratio is valid:
[tex]\frac{EF}{CE}=\frac{EG}{DE}[/tex]
Step 2: Substitute the value of the lengths of the sides into the ratio as follows:
[tex]\begin{gathered} EF=x \\ CE=27 \\ DE=25 \\ EG=40 \\ \text{Thus:} \\ \frac{EF}{CE}=\frac{EG}{DE} \\ \Rightarrow\frac{x}{27}=\frac{40}{25} \end{gathered}[/tex]
Step 3: Solve the resulting equation for x, as follows:
[tex]\begin{gathered} \frac{x}{27}=\frac{40}{25} \\ \Rightarrow x=\frac{40}{25}\times27=\frac{1080}{25}=43.2 \\ \Rightarrow x=43.2 \end{gathered}[/tex]
Therefore, the value of x is 43.2 (Option B)
