The area of a trapezium is \(200\text{ cm}^2\). Its parallel sides are in the ratio \(2 : 3\) and the perpendicular distance between them is \(16\text{ cm}\...

To find the lengths of the parallel sides of the trapezium, we need to use the formula for the area of a trapezium.
The formula for the area of a trapezium is:
Area = (1/2) * (sum of parallel sides) * (perpendicular distance between them).
In this case, we are given that the area of the trapezium is 200 cm² and the perpendicular distance between the parallel sides is 16 cm.
Let's assume the lengths of the parallel sides are 2x and 3x.
Using the formula, we can write the equation as:
200 = (1/2) * (2x + 3x) * 16
Simplifying the equation, we have:
200 = (5x) * 16
Dividing both sides by 5, we get:
40 = 4x
Dividing both sides by 4, we get:
10 = x
So, the length of one of the parallel sides is 2x = 2 * 10 = 20 cm.
And the length of the other parallel side is 3x = 3 * 10 = 30 cm.
Therefore, the correct answer is:
10 cm and 15 cm.