To solve this, we need to calculate the perimeter of the rectangle and then determine the ratio of the length to the perimeter.

Step 1: Calculate the perimeter of the rectangle

The formula for the perimeter $P$ of a rectangle is:
$P = 2(\text{length} + \text{width})$ Here, the length is $4$ inches, and the width is $7$ inches. Substituting these values:
$P = 2(4 + 7) = 2(11) = 22 \, \text{inches}$

Step 2: Determine the ratio

The ratio of the length to the perimeter is given by:
$\text{Ratio} = \frac{\text{Length}}{\text{Perimeter}}$ Substituting the values: $\text{Ratio} = \frac{4}{22} = \frac{2}{11}$

Final Answer:

The ratio of the length of the rectangle to the perimeter is: $\boxed{\frac{2}{11}}$

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Would you like further explanation on how this was calculated? Here are 5 related questions to expand your understanding:

1. What is the ratio of the width to the perimeter of the same rectangle?
2. If the dimensions of the rectangle were doubled, how would the ratio of the length to the perimeter change?
3. What is the ratio of the area of the rectangle to the perimeter?
4. How would the ratio change if the length and width were swapped?
5. Can you calculate the diagonal of the rectangle using the Pythagorean theorem?

Tip: Remember, a ratio compares two quantities, and it can often help identify relationships in geometry problems!