Answer:
The length of FE is √286 units.
Explanation:
Let the length of FE = x
Since FG is parallel to CD, then triangles EFG and ECD are similar triangles.
The ratio of the corresponding sides are:
[tex]\frac{FE}{CE}=\frac{FG}{CD}[/tex]
Substitute the given values from the diagram above:
[tex]\frac{x}{26}=\frac{11}{x}[/tex]
We then solve the equation for x.
[tex]\begin{gathered} \text{ Cross multiply} \\ x^2=26\times11 \\ \text{ Take the square root of both sides} \\ x=\sqrt{26\times11} \\ x=\sqrt{286} \\ \implies FE=\sqrt{286}\text{ units} \end{gathered}[/tex]
The length of FE is √286 units (in simplest radical form).
