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:
[tex]\frac{CE}{EB}=\frac{CD}{DA}[/tex]
Where,
[tex]\begin{gathered} CD=20 \\ DA=8 \end{gathered}[/tex]
Then,
Put the value into the above proportionality:
So,
[tex]\begin{gathered} \begin{equation*} \frac{CE}{EB}=\frac{CD}{DA} \end{equation*} \\ \frac{CE}{EB}=\frac{20}{8} \end{gathered}[/tex]
Then,
[tex]\begin{gathered} \frac{CE}{EB}=\frac{20}{8} \\ 8CE=20EB \\ CE=\frac{20EB}{8}...(1) \end{gathered}[/tex]
Now,
We need to find the value for EB:
So,
For EB:
[tex]\begin{gathered} \frac{BE}{BC}=\frac{AD}{AC} \\ \frac{BE}{35}\frac{8}{28} \\ 28BE=280 \\ BE=10 \end{gathered}[/tex]
Then,
Put the value of BE into the equation (1):
So,
[tex]\begin{gathered} \begin{equation*} CE=\frac{20EB}{8} \end{equation*} \\ CE=\frac{20(10)}{8} \\ CE=\frac{200}{8} \\ CE=25 \end{gathered}[/tex]
Final answer:
Hence, the value of CE is 25.
