Q34. - Geometry

Question

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

Step-by-Step Solution

Answer

The value of $x$ is 11.

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.