Explanation:

To find the sum of the lengths of the two parallel sides of a trapezium given its area and the distance between the sides, you can use the formula for the area of a trapezium:

$$ \text{Area} = \frac{1}{2} \times (\text{Sum of parallel sides}) \times \text{Height} $$

- You are given that the area is 100 cm².

- The height, which is the distance between the parallel sides, is 10 cm.

- Plug these values into the formula:

$$ 100 = \frac{1}{2} \times (\text{Sum of parallel sides}) \times 10 $$

- Simplify the equation:

$$ 100 = 5 \times (\text{Sum of parallel sides}) $$

- Solve for the sum of the parallel sides:

$$ \text{Sum of parallel sides} = \frac{100}{5} = 20 \, \text{cm} $$

- Therefore, the sum of the lengths of the two parallel sides is 20 cm.

- Option 3: 20 cm is the correct answer.