The difference between the length of two parallel sides of a trapezium is 12 cm. The perpendicular distance between these two parallel sides is 60 cm. If the area of the trapezium is 1380 cm², then find the length of each of the parallel sides (in cm).

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**Solution:**

1. Let the smaller parallel side be *x* cm.

2. Then the longer parallel side is *(x + 12)* cm.

3. The perpendicular distance (height) between the parallel sides is given as 60 cm.

4. The area of the trapezium is given by the formula:
   
   $$	ext{Area} = \frac{1}{2} 	imes (	ext{sum of parallel sides}) 	imes 	ext{height}$$

5. Substitute the known values:
   
   $$1380 = \frac{1}{2} 	imes (x + x + 12) 	imes 60$$

6. Simplify:
   
   $$1380 = 30 	imes (2x + 12)$$

$$\Rightarrow 2x + 12 = \frac{1380}{30} = 46$$

7. Solve for *x*:
   
   $$2x = 46 - 12 = 34$$

$$x = 17$$

8. Therefore, the longer side is:
   
   $$17 + 12 = 29$$

**Answer:** The lengths of the parallel sides are **29 cm** and **17 cm**.

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