The ratio of the length of the parallel sides of a trapezium is 3 : 2. The shortest distance between them is 15 cm. If the area of the trapezium is 1350 sq. cm, then find the difference of the lengths of the parallel sides.

Correct option is C

Given:
The ratio of the parallel sides of a trapezium is 3 : 2
Area of the trapezium is 1350 sq. cm.
The distance between two parallel side is 15 cm.
Formula Used:
Area of trapezium = $$\frac 12$$​ × (sum of parallel side)× distance between two parallel sides
Solution:
Let the parallel side of the trapezium be 3x and 2x
According to the question,
Area of trapezium = $$\frac 12$$​ × (sum of parallel side)× distance between two parallel sides
=> 1350 = $$\frac 12$$​ × (3x + 2x)× 15
=> $$\frac {5x}2$$​ = 90
=> x = 90 × $$\frac 25$$​​
=> x = 36 cm
Difference between two parallel side =  3 × 36 – 2 × 36 =  36 cm