Question

For the following figure, $E$is the midpoint of $\overline{DF}$. Find the value $y$, where $GE=y$, $EH=y-1$and$GH=11$

Short answer

The value of$x$ is 6.

Step-by-step solution

Step 1. Apply the concept of the length of the line.

The total length of the line is the sum of the length of all parts of a line.

Step 2. Check the figure.

Consider the figure.

Here the length of $GH$is the sum of $GE$ and$EH$

Step 3. Find the value of y.

Since$GH=GE+EH$

Equate the values as follows:

$\begin{array}{l}11=y+y-1\\ 11=2y-1\end{array}$

Step 4. Simplify the equation.

Simplify the equation as follows:

$$\begin{gathered} 11=2y-1 \\ 11+1=2y \\ \begin{array}{c}12=2y\\ y=6\end{array} \end{gathered}$$

Therefore, the value of$y$is 6.