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The ratio of the length of the parallel sides of a trapezium is 3 : 2. The shortest distance between them is 15 cm. If the area of the trapezium is 1350 sq. cm, then find the difference of the lengths of the parallel sides.
1. 95 cm
2. 21 cm
3. 36 cm
4. 65 cm

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Correct Answer - Option 3 : 36 cm

Given:

Ratio of the length of the parallel sides of a trapezium = 3 : 2

Height of trapezium = 15 cm

Area of trapezium = 1350 cm2

Formula used:

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

Calculations:

Let the length of parallel sides be 3x and 2x.

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

⇒ (5x/2) × 15 = 1350

⇒ 75x/2 = 1350

⇒ x = 36

Difference of parallel sides = 3x - 2x = x = 36 cm

∴ The difference of the lengths of the parallel sides is 36 cm.

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