The parallel sides of a trapezium are in the ration 3:4 and the perpendicular distance between them is 12 cm. If the area of the trapezium is 630 cm², then its shorter length of the parallel sides is

Given

Lengths of the parallel sides are in the ratio 3:4

Therefore let one of the side length be 3X and other side length be 4X

Area of trapezium= 630 cm²

Let Height (h) =12 cm

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

Therefore Area of trapezium is × (3X +4X) × 12 =630 cm².

× (3X + 4X) × 12 = 630

⇒(7X) × 6 =630

⇒ 42X = 630

⇒ X = = 15

.^.. length of the parallel sides is 3X = 3 × 15 =45 cm and 4X = 4 × 15 = 60 cm.

Therefore shortest length of the parallel sides is 45 cm.