The difference between the lengths of two parallel sides of a trapezium is 6 cm. The perpendicular distance between them is 24 cm. If the area of the trapezium is 648 cm², then what is the length of the parallel sides?​

Correct option is B

Given:

Difference between the lengths of two parallel sides of a trapezium = 6 cm

Perpendicular distance (height) = 24 cm

Area of the trapezium = 648 cm²

Find the lengths of the parallel sides.

Formula Used:

Area of a trapezium = $$\frac{1}{2}$$​ × sum of parallel sides× height

Solution:

Let the parallel sides be x cm and x + 6 cm

Using the area formula:

648 = $$\frac{1}{2} \times (x + x + 6) \times 24$$​​

648 = 12(2x + 6)

648 = 24x + 72

24x = 576

x = 24

So, the lengths of the parallel sides are: 24 cm and 30 cm