The area of a trapezium is 384 cm². Its parallel sides are in the ratio 5:3 and the distance between them is 12 cm. the longer of the parallel sides is

Given

Lengths of the parallel sides are in the ratio 5:3

Therefore let one of the side length be 5X and other side length be 3X

Area of trapezium= 384 cm²

Let Height (h) =12 cm

We know that area of trapezium is × (sum of parallel sides) × height

Therefore Area of trapezium is × (5X +3X) × 12 =384 cm².

× (5X + 3X) × 12 =384

⇒ (8X) × 6 =384

⇒ 48X = 384

⇒ X = = 8

.^.. length of the parallel sides is 5X=5 × 8 =40 cm and 3X = 3 × 8 = 24 cm.

Therefore length of the longest side is 40 cm.