Question

For the following figure, $E$is the midpoint of $\overline{DF}$. Find the value $x$, where $DE=45$and$EF=5x-10$

Short answer

The value of$x$ is 11.

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:

$$\begin{gathered} 45=5x-10 \\ 45+10=5x \\ 55=5x \\ x=11 \end{gathered}$$

Therefore, the value of$x$ is 11.