Q33 - Geometry

Question

For the following figure, E is the midpoint $\overline{DF}$. Find the value x, where $DE=5x+3$ and $EF=33$.

Step-by-Step Solution

Answer

The value of x is 6.

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:

$\begin{array}{l} 33=5x+3\\ 33-3=5x\\ 30=5x\\ x=6\end{array}$

Therefore, the value of x is 6.