The parallel sides of a trapezoid are 3 cm and 9 cm. The non-parallel sides are 4 cm and 6 cm. A line parallel to the bases divides the trapezoid into two trapezoids of equal perimeters. The ratio in which each of the non- parallel sides is divided is ?

Given that: ABCD is a trapezoid and EF || AB

Let

And,

Since, the line parallel to the base divides the two non- parallel lines in the same ratio.

So,

Given: perimeters of both trapezoids is same

So,

Solving equation (1) and (2), we get,

Thus,

The ratio in which each of the non- parallel sides is,

Thus, the ratio in which each of the non- parallel sides is 4:1