Explanation:

- Let's define the sides of the rectangle as \(a\) (smaller side) and \(b\) (larger side).

- The distance walked along two sides is \(a + b\).

- The diagonal distance using the Pythagorean theorem is \(\sqrt{a^2 + b^2}\).

- It's given that by walking diagonally, a distance equal to \(\frac{1}{4}\) of the larger side \(b\) would be saved.

- So, \(a + b - \sqrt{a^2 + b^2} = \frac{b}{4}\).

- Rearranging, \(\sqrt{a^2 + b^2} = a + \frac{3b}{4}\).

To find the ratio of \(b\) to \(a\):

1. Substitute the given options into the equation \(\sqrt{a^2 + b^2} = a + \frac{3b}{4}\) to find which one satisfies the equality.

2. For option 1 (\(\frac{b}{a} = \frac{7}{24}\)), it doesn't satisfy.

3. For option 2 (\(\frac{b}{a} = \frac{11}{18}\)), it doesn't satisfy.

4. For option 3 (\( \frac{b}{a} = \frac{24}{7} \)), it satisfies the equation.

5. For option 4 (\(\frac{b}{a} = \frac{18}{11}\)), it doesn't satisfy.