- Define the length as \(L\) and width as \(W = 18\).
- Translate the relationship "width is one-sixth the length" into the equation \(\frac{L}{6} = 18\).
- Solve for \(L\) by multiplying both sides by 6, yielding \(L = 108\).
- Final answer: \(\boxed{\frac{L}{6} = 18; L = 108 \text{ inches}}\).
Explanation
- Setting up the Equation
We are given that the width \(W\) of a rectangular poster is \(18\) inches. The problem states that the width is one-sixth of its length \(L\). This relationship can be expressed mathematically as:
\[W = \frac{L}{6}\]
Substituting the known width \(W = 18\) into this expression gives us the equation:
\[\frac{L}{6} = 18\]
- Solving for the Length
To determine the length \(L\), we solve the equation \(\frac{L}{6} = 18\) by isolating \(L\). We multiply both sides of the equation by \(6\):
\[L = 18 \times 6\]
\[L = 108\]
Thus, the length of the poster is \(108\) inches.
- Conclusion
Comparing our results to the given options:
- \(6L = 18, L = 3\)
- \(\frac{L}{6} = 18; L = 108\)
- \(6 + L = 18; L = 12\)
- \(L - 6 = 18; L = 24\)
Our equation \(\frac{L}{6} = 18\) and solution \(L = 108\) match the second option. Therefore, the correct representation and result is \(\frac{L}{6} = 18; L = 108\) inches.
Examples
Understanding how to relate dimensions through fractions and algebraic equations is a fundamental skill in design, architecture, and everyday DIY projects. For instance, if you are building a custom shelf where the depth must be a specific fraction of the length to maintain structural balance, setting up an equation like this ensures your measurements are correct and proportional before you begin cutting materials. Applying these simple algebraic steps helps in precise planning and problem-solving in various real-world tasks.