Explanation:

- The perimeter of the rectangle is given as 68 cm.

- The formula for the perimeter is 2(l + w) = 68. Simplifying, l + w = 34.

- The area of the rectangle is given as 240 cm².

- The formula for the area is l × w = 240.

- You have two equations: l + w = 34 and l × w = 240.

- Solve these equations simultaneously to find l and w.

- From l + w = 34, express w = 34 - l.

- Substitute in the area equation: l(34 - l) = 240.

- This expands to a quadratic equation: l² - 34l + 240 = 0.

- Solving gives l = 20 cm or l = 12 cm, leading to w = 14 cm or w = 18 cm.

- Calculate the diagonal using the Pythagorean theorem: v(l² + w²).

- Using either dimension: v(20² + 14²) = v(400 + 196) = v596 ˜ 24.42 cm or v(18² + 12²) = v(324 + 144) = v468 ˜ 21.63 cm.

- None of the given options match exactly, but if approximating, none are close to 24.42 cm or 21.63 cm. Please check the problem or options again.

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