Explanation:

- To find the diagonal of the rectangle, first determine the dimensions of the rectangle.

- The perimeter of the rectangle is equal to the length of the wire, which is 168 cm.

- Given that the sides of the rectangle have a ratio of 5:7, we let the sides be 5x and 7x.

- The perimeter formula for a rectangle is: 2(length + width) = Perimeter.

- Plugging the values in, we get: 2(5x + 7x) = 168 cm.

- Simplifying gives: 24x = 168.

- Solving for x, we get x = 7.

- Therefore, the sides are 35 cm and 49 cm.

- Calculate the diagonal using the Pythagorean theorem: v(35² + 49²).

- This gives v3626.

- The correct answer is Option 4: v3626.

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