Question

The area of a trapezium is 150 cm². The parallel sides are in the ratio 2 ∶ 3 and the perpendicular distance between them is 15 cm. Find the length of shorter parallel side.

1. 6 cm
2. 9 cm
3. 8 cm
4. 12 cm

Answer 1

Correct Answer - Option 3 : 8 cm

Given:

Parallel sides are in the ratio = 2 ∶ 3

Distance between the parallel sides = 15 cm

Area of trapezium = 150 cm²

Formula used:

Area of a trapezium \(= \frac{1}{2}\left( {a + b} \right) \times d\)

Where,

a, b = Two parallel sides

d = Distance between the two parallel sides

Calculations:

Let the parallel sides be 2x and 3x

Area of trapezium = (1/2) × (2x + 3x) × 15

⇒ (1/2) × (2x + 3x) × 15 = 150

⇒ (1/2) × 5x = 10

⇒ 5x = 20

⇒ x = 4

The parallel sides of trapezium:

⇒ 2x = 8 cm

⇒ 3x = 12 cm

∴ The length of shorter parallel side is 8 cm