Q35. - Geometry

Question

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

Step-by-Step Solution

Answer

The value of $x$ is 3.

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.