Question

In the diagram below, FG is parallel to CD. If the length of CD is the same as the length of FE, CE = 26, and FG = 11, find the length of FE. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.

Answer 1

When stated in a simple radical form, the length of FE would be =√286.

How to determine the length of the triangle?

To determine the missing length of the triangle, the following steps should be taken as follows:

The ratio of the corresponding length is given thus

FE/CE = FG/CD

where;

FE = X

CE = 26

FG = 11

CD = X

That is

X /26 = 11/X

x² = 26×11

X = √286

Answer 2

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:

`(FE)/(CE)=(FG)/(CD)`

Substitute the given values from the diagram above:

`(x)/(26)=(11)/(x)`

We then solve the equation for x.

`\begin{gathered} \text{ Cross multiply} \\ x^2=26*11 \\ \text{ Take the square root of both sides} \\ x=√(26*11) \\ x=√(286) \\ \implies FE=√(286)\text{ units} \end{gathered}`

The length of FE is √286 units (in simplest radical form).