Question

For the following figure, $E$is the midpoint of $\overline{DF}$. Find the value $x$, where $DE=3x$and$EF=x+6$

Short answer

The value of$x$ is 3.

Step-by-step solution

Step 1. Apply the concept of midpoint.

The midpoint of a line divides the line into two equal parts.

Step 2. Check the figure.

Consider the figure.

Here $E$is the midpoint of $\overline{DF}$.

Therefore $DE=EF$.

Step 3. Find the value of x.

Since $DE=EF$.

Equate the values as follows:

$$\begin{gathered} 3x=x+6 \\ 3x-x=6 \\ 2x=6 \\ x=3 \end{gathered}$$

Therefore, the value of$x$ is 3.