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.

Step-by-step 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:

`(CE)/(EB)=(CD)/(DA)`

Where,

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

Then,

Put the value into the above proportionality:

So,

`\begin{gathered} \begin{equation*} (CE)/(EB)=(CD)/(DA) \end{equation*} \\ (CE)/(EB)=(20)/(8) \end{gathered}`

Then,

`\begin{gathered} (CE)/(EB)=(20)/(8) \\ 8CE=20EB \\ CE=(20EB)/(8)...(1) \end{gathered}`

Now,

We need to find the value for EB:

So,

For EB:

`\begin{gathered} (BE)/(BC)=(AD)/(AC) \\ (BE)/(35)(8)/(28) \\ 28BE=280 \\ BE=10 \end{gathered}`

Then,

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

So,

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

Final answer:

Hence, the value of CE is 25.