Concept:Area of a trapezium.Explanation:We are given a trapezium where the parallel sides are in the ratio 2:5. Let the lengths of these parallel sides be $2x$ cm and $5x$ cm, respectively. The distance between these parallel sides (which is the height of the trapezium) is given as $h = 10$ cm. The area of the trapezium is given as $A = 350$ cm$^2$.The formula for the area of a trapezium is:$$A = \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}$$Substituting the given values and our assumed lengths:$$350 = \frac{1}{2} \times (2x + 5x) \times 10$$$$350 = \frac{1}{2} \times (7x) \times 10$$$$350 = 7x \times 5$$$$350 = 35x$$To find the value of $x$, we divide both sides by 35:$$x = \frac{350}{35}$$$$x = 10$$Now we can find the lengths of the parallel sides:Length of the first parallel side = $2x = 2 \times 10 = 20$ cm.Length of the second parallel side = $5x = 5 \times 10 = 50$ cm.Answer:The lengths of the parallel sides are 20 cm and 50 cm.