If 

*QR* = 9

, 

*RS* = *x* + 3

, and 

*QS* = 3*x*

, what is *QS*?

We are given the following:

- \( QR = 9 \)
- \( RS = x + 3 \)
- \( QS = 3x \)

Since \( QR \), \( RS \), and \( QS \) represent the lengths of line segments on a straight line, we can use the relation:

\[
QS = QR + RS
\]

Substituting the given values:

\[
3x = 9 + (x + 3)
\]

Simplifying the equation:

\[
3x = 9 + x + 3
\]

\[
3x = x + 12
\]

Subtract \( x \) from both sides:

\[
2x = 12
\]

Now, divide by 2:

\[
x = 6
\]

Finally, substitute \( x = 6 \) back into the expression for \( QS = 3x \):

\[
QS = 3(6) = 18
\]

So, \( QS = 18 \).

Would you like further details or have any questions?

Here are 5 related questions:
1. If \( QS = 18 \) and \( QR = 9 \), what is \( RS \)?
2. If \( RS = x + 3 \) and \( x = 6 \), what is the length of \( RS \)?
3. How does changing the value of \( x \) affect the length of \( QS \)?
4. If \( QR \) were doubled, what would be the new value of \( QS \)?
5. What happens to \( QS \) if \( QR = 2x \) instead of \( 9 \)?

**Tip:** When solving for variables in geometry problems, always substitute back into the original expressions to check your work.

Learn how to solve a geometric problem involving line segments QR, RS, and QS. Given QR = 9, RS = x + 3, and QS = 3x, find the length of QS using algebraic equations and geometric principles. Suitable for students in Grades 9-10.

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