Question

The parallel sides of a trapezium are in the ratio 3 ∶ 5 and the perpendicular distance between them is 12 cm. The area of trapezium is 240 cm². Find the length of the shorter side of the trapezium?
1. 21 cm
2. 12 cm
3. 18 cm
4. 15 cm

Answer 1

Correct Answer - Option 4 : 15 cm

Given:

Ratio of Parallel sides = 3 ∶ 5

Area of trapezium = 240 cm²

Height of trapezium = 12 cm

Concept:

Replace the ratio with a constant and using the formula for the area of the trapezium, calculate the sides of the trapezium.

Formula used:

Area of trapezium = 1/2 × (Sum of parallel sides) × height

Calculation:

Let the parallel sides be 3x and 5x

Area of trapezium = 1/2 × (Sum of parallel sides) × height

⇒ 240 cm² = 1/2 × (3x + 5x) × 12 cm

⇒ 240 cm² = (1/2) × (8x) × 12 cm

⇒ 8x = (240 × 2)/12 cm

⇒ x = 40/8 cm

⇒ x = 5 cm

Shorter parallel side of the trapezium = 3x = 3 × 5 cm = 15 cm.

∴ Shorter parallel side of the trapezium is 15 cm.