Q37. - Geometry

Question

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

Step-by-Step Solution

Answer

The value of $x$ is 6.

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.