In trapezium PQRS, PQ || SR and the ratio of PQ to SR is 3:2. If the area of the trapezium is 480 cm² and the distance between PQ and SR is 12 cm, then the length of SR is

The correct answer is 32 cm.

We are given the following information about the trapezium PQRS:

- The parallel sides are PQ and SR, with PQ || SR.
- The ratio of the lengths of PQ to SR is 3:2.
- The area of the trapezium is 480 cm².
- The distance between the parallel sides (height, h) is 12 cm.

Let the common ratio multiplier be x. Then:
PQ = 3x
SR = 2x

The formula for the area of a trapezium is given by:

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

Substitute the given values into the formula:

$480=\frac{1}{2}\times (3x+2x)\times 12$

Simplify the equation:

$480=\frac{1}{2}\times 5x\times 12$

$480=5x\times 6$

$480=30x$

Solve for x:

$x=\frac{480}{30}$

$x=16$

Now, calculate the length of side SR:

$\text{SR}=2x=2\times 16=32\text{cm}$

Thus, the length of SR is 32 cm.