Let's solve the problem step by step.

Given:

1. The ratio of the length to the width for both rectangles X and Y is $\frac{L}{W} = \frac{6}{5}$.
2. The width of rectangle X is 19.1 times the width of rectangle Y, i.e., $W_X = 19.1 \times W_Y$.

To Find:

We need to determine how the length of rectangle X compares to the length of rectangle Y.

Solution:

1. Step 1: Express the lengths in terms of widths:

   Since the ratio of length to width for both rectangles is $\frac{6}{5}$, we can express the lengths of the rectangles as: $L_X = \frac{6}{5} \times W_X$ $L_Y = \frac{6}{5} \times W_Y$

2. Step 2: Substitute $W_X = 19.1 \times W_Y$ into the equation for $L_X$:

   $L_X = \frac{6}{5} \times (19.1 \times W_Y)$

3. Step 3: Simplify to compare $L_X$ with $L_Y$:

   $L_X = 19.1 \times \frac{6}{5} \times W_Y$ $L_X = 19.1 \times L_Y$

Conclusion:

The length of rectangle X is 19.1 times the length of rectangle Y.

Correct Answer:

The length of rectangle X is 19.1 times the length of rectangle Y.

Would you like further details or have any other questions?

Here are five related questions to deepen your understanding:

1. How do you calculate the area of a rectangle given its length and width?
2. If the ratio of the width to the length changes, how does it affect the comparison of the areas?
3. Can you find the perimeter of rectangle X given its width and length?
4. How does changing the ratio of length to width affect the shape of a rectangle?
5. If the widths of both rectangles were equal, how would their lengths compare?

Tip: When dealing with ratios and proportions, it's often helpful to express one variable in terms of another to make comparisons easier.