Question

The area of a field in the shape of a trapezium measures 1440 m². The perpendicular distance between its parallel sides is 24 m. If the ratio of the parallel sides is 5 : 3, the length of the longer parallel side is:
1. 75 m
2. 45 m
3. 120 m
4. 60 m

Answer 1

Correct Answer - Option 1 : 75 m

Given:

Area of field = 1440 m²

The perpendicular distance between parallel sides = 24 m

The ratio of parallel sides = 5 : 3

Formula Used:

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

Calculation:

Let the parallel sides be 5x and 3x respectively.

Area of trapezium = 1440

⇒ 1/2 × (5x + 3x) × 24 = 1440

⇒ 12 × (8x) = 1440

⇒ 96 x = 1440

⇒ x = 1440/96 = 15

Longer side = 5x = 75 m

∴ The length of the longer side is 75 m.