For each oftwo rectangles,the ratio of the rectangle's length to i; width is 6 to 5.The width ofrectangle Xis 19.1 times the width

frectangle Y. How does the length ofrectangle Xcompare to the length ofrectangl

Y?

The length ofrectangle Xis 0.83times the length ofrectangle Y

The length ofrectangle X is 1.2times the length ofrectangle Y

The length ofrectangle Xis 19.1times the length ofrectangle Y.

The length ofrectangle X is 22.92times the length ofrectangle Y.

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.

Learn how to compare the lengths of two rectangles with given length to width ratios and width proportions. Solve a problem involving rectangles X and Y where the width of X is 19.1 times the width of Y, and the length of X is related to the length of Y. Understand the application of ratio and proportion in geometry. Suitable for Grades 7-9.

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