Question

Complete the statement needed to find the missing value then find the missing value. CE =

Answer 1

Given:

There are given that the triangle ABC.

Explanation:

According to the given triangle:

We can see that the given triangle represents the proportionality theorem:

That means:

If a line parallel to one side of the triangle intersects the other two sides of the triangle, then the line divides these two sides proportionality.

Then,

From the given triangle:

$\frac{CE}{EB}=\frac{CD}{DA}$

Where,

$\begin{gathered} CD=20 \\ DA=8 \end{gathered}$

Then,

Put the value into the above proportionality:

So,

$\begin{gathered} \begin{equation*} \frac{CE}{EB}=\frac{CD}{DA} \end{equation*} \\ \frac{CE}{EB}=\frac{20}{8} \end{gathered}$

Then,

$\begin{gathered} \frac{CE}{EB}=\frac{20}{8} \\ 8CE=20EB \\ CE=\frac{20EB}{8}...(1) \end{gathered}$

Now,

We need to find the value for EB:

So,

For EB:

$\begin{gathered} \frac{BE}{BC}=\frac{AD}{AC} \\ \frac{BE}{35}\frac{8}{28} \\ 28BE=280 \\ BE=10 \end{gathered}$

Then,

Put the value of BE into the equation (1):

So,

$\begin{gathered} \begin{equation*} CE=\frac{20EB}{8} \end{equation*} \\ CE=\frac{20(10)}{8} \\ CE=\frac{200}{8} \\ CE=25 \end{gathered}$

Final answer:

Hence, the value of CE is 25.