The parallel sides of a trapezium are in the ratio 3 : 4. If the distance between the parallel sides is 9 dm and its area is 126 dm², find the lengths of its parallel sides.

Given:

The parallel sides of a trapezium are in the ratio 3 : 4.

The distance between the parallel sides = 9 dm

The area = 126 dm²

Let the parallel sides of trapezium be 3a and 4a.

As we know, the area of a trapezium = $\dfrac{1}{2}$ x (sum of parallel side) x height

⇒ $\dfrac{1}{2}$ x (3a + 4a) x 9 = 126

⇒ $\dfrac{1}{2}$ x 7a x 9 = 126

⇒ $\dfrac{1}{2}$ x 63a = 126

⇒ 63a = 126 x 2

⇒ 63a = 252

⇒ a = $\dfrac{252}{63}$

⇒ a = 4

So, the parallel sides of the trapezium are:

For 3a:

= 3 x 4 dm = 12 dm

And, for 4a:

= 4 x 4 dm = 16 dm

Hence, the lengths of its parallel sides are 12 dm and 16 dm.