Question

The area of a trapezium is 540 cm². If the ratio of its parallel sides is 5 : 7 and the distance between the parallel sides 18 cm, find the length of the parallel sides.

Answer 1

Given: Area = 540 cm²; ratio of parallel sides = 5 : 7; distance (height) between parallel sides = 18 cm.

Step-wise calculation:

1. Let the parallel sides be 5x cm and 7x cm.

2. Area of a trapezium = `1/2` × sum of parallel sides × height.

3. Substitute values:

`540 = 1/2 xx (5x + 7x) xx 18`

4. Simplify:

`540 = 1/2 xx 12x xx 18`

= 108x

5. Solve for x:

`x = 540/108`

= 5

6. Therefore, the parallel sides are 5x = 5 × 5 = 25 cm and 7x = 7 × 5 = 35 cm.

The lengths of the parallel sides are 25 cm and 35 cm.