Q4. - Geometry

Question

When $\mathbf{RN}\mathbf{=}\mathbf{7}$, $\mathbf{NC}\mathbf{=}\mathbf{3}\mathbf{x}\mathbf{+}\mathbf{5}$ and $\mathbf{RC}\mathbf{=}\mathbf{18}$, what is the value of $\mathbf{x}$?

Step-by-Step Solution

Answer

The value of $x$ is 2.

Step 1. Write the Segment Addition Postulate.

The Segment Addition Postulate states that: 

If a point $\mathrm{B}$ lies between the points $\mathrm{A}$ and $\mathrm{C}$ then $\mathrm{AB}+\mathrm{BC}=\mathrm{AC}$.

Step 2. Draw the diagram.

The given diagram is:

Step 3. Write the equation expressing the relation between RN, NC, and RC by using the Segment Addition Postulate.

From the given diagram it can be noticed that:

The point $N$ is lying between the points $R$ and $C$.

Therefore, by using the segment addition postulate:

$RN+NC=RC$

Step 4. Substitute the values of RN, NC, and RC in the above equation.

$\begin{array}{l}RN+NC=RC\\ 7+3x+5=18\end{array}$

Step 5. Solve the above equation to find the value of x.

$\begin{array}{l}3x+12=18\\ 3x=18-12\\ 3x=6\\ x=2\end{array}$

Therefore, the value of $x$ is 2.