# 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

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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

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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.